But up until now there's been no ambiguity as to the Classic and Nu eras taking place in the same universe. Classic Doctors have even showed up in NuWho
There is lots of ambiguity in the following ways. Be warned this is a long post, but I suppose I should cram all of these arguments into one post together so I can just refer to or copy and paste this whenever necessary LOL.
New Who and Classic Who are comparable to the Gary Oldman and Christopher Lee Dracula in that both are based on the same basic idea, and use the necessary, recognizable iconography making them adaptations or versions of what is clearly the one story/character. However they can't be linked in universe because there are too many contradictions from a practical point of view. Also even though they are from the same idea they are still aimed at different audiences, and they have nothing to do with each other in terms of production, or the generation and zeitgeist they were made in. It's fine for them to be that different BTW. They should be as that's how characters like Dracula and Sherlock Holmes survive and adapt. In a remake you can and should be more flexible as long as you stick to the very, very basic idea unlike a sequel. Also Oldman has no impact on Lee because he is a different universe. Everybody wins this way, as fans of Lee and Oldman are not obligated to watch the other, but people who love the idea of Dracula and want to see it reimagined in lots of different ways can appreciate both.
Now where New Who is different to the two Dracula's is I feel RTD either through loyalty to classic who, or to cash in on it, or perhaps a bit of both, tried to make it a sequel whilst essentially writing it as a reboot. He tried to get away with this and get the best of all worlds, through member berries and saying the classic show had no continuity, was all about change so it doesn't make a difference. This worked for a while, but in the end it caused both series to devour each other. On the one hand anything classic who related had to have new who things crowbarred in like Scratchman, its history has to be rewritten in factual articles to Delgado wanted to bang Pertwee to make it fit with new who. Meanwhile New Who has to drown in classic who member berries to still keep classic who fans around. End result? Classic Who fans fall out of love with the original as it no longer has an identity, and new viewers are put off by the mountain of references that are now in place of it having a stable identity.
Meanwhile the differences between them.
1/ The Doctors character: In classic who regeneration is presented as an advanced form of healing rather than a full on rebirth. His body breaks down, it repairs itself and as a result his body and outer persona change. However his core personality, consciousness, memories are all unchanged. The differences between the Doctors from classic who's personality are comparable to the changes we all go through in life only more noticable and rapid. The attitude in classic who was never. "He completely changes." It was always "let's get an actor in who will bring something new to it, but not change it too much that you can't imagine it is still Hartnell under the new face." Terrance Dicks, Robert Holmes, JNT and all the actors who played the Doctor said as much, and when you watch the show that's clearly how it is presented.
All of the classic Doctors are mysterious about their past, all travel the universe because they enjoy exploring new planets, learning about new cultures, all love the life they are living, all of them are quite old and wise and mature and even cold in some ways, like when it comes to dealing with death and loss. However all can be quite childish and selfish when it comes to getting their own way and prefer to do things on their own times. All have the same basic moral code, where they will kill if need be, but prefer peaceful solutions. All have a sense of mystery about them. All are asexual (we know the Doctor had a wife and he does seem to like Romana another Time Lady, but certainly he is asexual to human women and is more of a crazy old uncle/stern mentor to them. All of the Doctors are a jack of all trades master of none and have some fighting skills, but are not superhuman. Even their regeneration powers are toned down. Even physically they have similarities. They all have big unmanagable hair, dress in Victorian/Edwardian era clothing, wear frock coats and their are a number of motifs that run throughout all of their clothes, like hats (all but six) scarfs (1, 2, 4) capes (1, 2, 3 and 6) and question mark lapels (4, 5, 6, 7.)
Finally in the classic era the Doctor tended to be played by a more striking, unconventional character actor who at that point in his career was typecast as outrageous comedy actors, villains or eccentric bit parts. Davison was the one exception, but even then he still played it as an old man in a young man's body.
In the revival meanwhile they say that the Doctor does die when he regenerates. There is no ambiguity about it. Tennant outright says his mind vanishes, and only the memories remain. New Who Doctors are akin to the Trill in Star Trek. Peter Capaldi also says he will die when Jodie comes and his last words are that he lets her go, IE she is waiting to come out. Meanwhile in Jodie's time we saw the other Doctors still exist in her mind in a kind of weird quasi afterlife as separate beings to her.
Also none of them really have any of the Doctors core traits. Eccelston Tennant and Smith don't travel because they want to see the universe. They travel because their planet is gone, and would rather have a normal life but there is no one to settle down with. They are less mysterious and talk about their past more like their love lives, and wedding and being a dad. Their moral codes are also more erratic and they have a phobia about guns and won't use them even in the most practical scenario, yet they also go too far the other way and kill enemies because they hate them if they are pissed off enough. They are also more emotional and fragile, and can't cope with loss and death and have breakdowns when their companions leave to the point where they carry out a genocide, quit being the Doctor and go through billions of years of torture if they lose a companion. They also fall in love with their female companions from Rose to Clara to River to Yaz.
Their powers and skills seem to be a bit different too. The new who Doctors seem to have 0 fighting skills, apart from Capaldi and surprisingly Jodie. Even then those two combined don't do nearly as much fighting as Hartnell alone! Also neither are as impressive as the classic Doctors who could take down multiple armed people at once. This is why they rely on the sonic more. At the same time however, they seem to be stronger being able to survive falls of 30 feet onto jagged rocks and falls from 100s of feet onto a marble floor, when lesser falls onto grass killed Tom, and their regeneration powers destroy TARDIS', buildings and Dalek fleets!
Even physically they don't match. They all Smith and a few of Capaldi's costumes aside dress in modern clothes, toned down clothes, like leather coats, hoodies, modern hipster coats, usually have shorter hair, and all but Capaldi are more conventional actors. The types you could imagine starring in soap operas, rom coms etc. The modern actors you would cast for a classic Doctor are the likes of Jason Watkins, Julian Barrat, Julian Richings etc. (Though that's not to say that the modern actors are worse actors than the classic boys. I actually think David Tennant is a better actor than Sylvester McCoy overall, but again McCoy is obviously more naturally quirky.)
The Master: Oh dear god! Where to begin? The Master in Classic Who much like the Doctor had a template to his personality. He was obsessed with gaining power over the universe because he felt he would bring order to the galaxy, even arguing that it would be better under his rule in the Daemons, Colony in Space. Of course that is bollocks as he is really a narcissistic sociopath who just loves having power over people. We see this in the way he loves manipulating people. He'll often twist the minds of anyone by preying on their weaknesses, or maybe even twisting their strengths, like Trenchard, Gaia, Kassia, Goth, Chang. If he can he'll even get them to love him, just so he can have more power. He also loves hypnotising people and putting them under his control that way. His main powers are hypnosis and the power to shrink people. He is also a smooth operator, very charming, suave and often greases his way into a position of authority and will take advantage of any prejudices, and problems in a society he can.
The Master is also a coward who will sacrifice anything to save his own life, isn't too proud to beg, and he develops a pathological hatred of the Doctor. At first he does have a respect for him and is even happy for the Doctor to help him build his better world, but the more the Doctor foils him and distracts him with his feud, the more he comes to despise the Doctor and soon becomes obsessed with not just killing, but torturing and humiliating the Doctor. We see this develop in Delgado's time, as by the Sea Devils he is already willing to cause a double genocide to f*ck the Doctor over.
Contrary to popular belief they were never close friends. It is mentioned in ONE story that they used to be friends, and the Doctor does express some regret at how the Master turned out. That's it however. It's mentioned in one other story that they knew each other. Five Doctors, and that story goes out of its way to show that their friendship didn't mean much to either as the first Doctor doesn't recognise him, whilst the third doctor does, showing it's not just because he is in a new body. The Doctor also has no affection for him, and tries to kill the Master dozens of times from Pertwee on. He does spare him a few times when he is unarmed, but he does that for all his foes, including Davros. He even says the Master is the one person he would wish death on. That's what makes the Master/Doctor feud so intense. They are an unstoppable force meets an immovable object. Neither really wins. On the one hand the Doctor stops him from taking over, but on the other he isn't able to stop the Master from causing untold death and suffering, even worlds being destroyed, and his friends loved ones dying at the Masters hands, whilst the Master always slips away unpunished.
Finally there is a story arc where the Master slowly loses his grip. Whilst he is always a sociopath, he slowly loses his mind after the accident robs him of his lives and reduces him to a burned out husk, and coupled with his hatred of the Doctor and failure of a life, he becomes more hateful, twisted, bitter and needlessly cruel.
In New Who however? The Master was always insane due hearing drumming in his head from when he was a child, he and the Doctor were best friends, possibly lovers. Tennant says it would be his honour to travel with the Master, despite him you know, blowing up a quarter of the universe, killing his friends loved ones etc he seems to have forgotten or doesn't give a shit about Nyssa and Tegan. Missy meanwhile is a joke as there is NOTHING of the Master in her. She is in love with the Doctor, she doesn't care about power (she even gives up an army of Cybermen because she doesn't care about power. Compare that to Delgado, Ainley and the burned Master who all gambled with the universe to control it.) She has no hypnotic powers, no shrinking ray, she isn't particularly manipulative. The closest we get is Chang, but he just works for her and we don't explore their relationship or dynamic like even Trenchard. She also isn't suave or charming. She's unbelievably crass making jokes about kissing uglies and people smelling, flips accents, is extremely annoying and CRAAAAAZZZZZZY. Dhawan is the closest (apart from Jacobi who was there for two mins.) Even then however he is too craaaaaaazzzzzyyyyy too, and his plan to blow up the universe is not very Masterish at all.
Finally much like the Doctor each of the new who Masters are different people anyway, hence why he can go from loving the Doctor to hating him, and he can can from a wife beating misogynist "is the future going to be all girl." To a misandrist "Time Lady some of us can afford the upgrade."
3/ Cybermen: In the original they were a single race from Mondas who became machine creatures to survive and after their planet was destroyed they fled to Telos and from there tried to rebuild and are portrayed as a dying, desperate race. In New Who Cybermen are a collective name given to thousands of unrelated humanoids who by coincidence became Cybermen, and there is no connection between those from Mondas and Telos, even though BOTH Telos stories revolve entirely around them having fled there from Mondas and struggling as a result on this new planet!
4/ Daleks: Actually they haven't been messed up as badly, but even then Moffat is responsible for a huge gaffe. In the season 9 story we find out that the Daleks have a concept of mercy, and always have done, which flies in the face of arguably their defining moment from Genesis where we learn they have no concept of pity.
Other villains/Lore: In old Who the Zygons home planet was destroyed by a solar flare, in New Who it was destroyed in the Time War, the Great Intelligence in classic who enters our world in the 16th century via a monks mind when he meditates. I then possesses him and for the next 400 years in Tibet, builds Yeti robots and a machine to allow it to fully enter our world, before the Doctor sends it back to its universe in the 1930s. It returns in the 1970s when Travers accidentally reactivates one of its robots, after which it creates an army of Yetis to conquer London before the Doctor sends it back into space. It is also portrayed as cold, logical and cowardly.
In New Who it is created in the 19th century by Walter Simeon. He has psychic powers that he doesn't know about and projects his anger, sorrow and bitterness into a snowman until it forms into an entity. He then nurtures it for decades until it is ready to survive on its own. It continues to feed on minds for decades until it is finally strong enough to leave the earth in the year 2013. It is also insane, hateful, and kills itself to get back at the Doctor.
Also in classic who people became aware of aliens in 1986 thanks to the Cyber invasion, whilst obviously nobody knows them in the 21st century. Also technology in the 1970s, 1980s in classic who is more advanced than technology in the 21st century earth. For instance the Ambassadors of Death involves people already travelling to Mars.
Finally on top of all of these huge inconsistencies Classic Who is just a very different show. It runs in a serialised format and takes its time to tell a story, it focuses on adventure, derring do, and the sci fi elements. It also mostly features stand alone stories in terms of seasons, but has stronger continuity running throughout it in the background like UNIT, the exile, Davros arc that spans multiple Doctors. New Who meanwhile tells shorter, snappier stories, favors story arcs, whilst it tends to reject long term developments like earth being aware of aliens, and it is more of a sci soap opera, like Buffy or Spider-Man. Again nothing wrong with that, I love both shows, but it's obviously different to classic who. New Who will often push the sci fi to the side and focus more on the companions everyday life.
With this in mind, it's fair to say that New Who is not a proper sequel, with the member berries nice as they may be, being nothing but feeble attempts to fuse them together. New Who works best as a loose sequel that can largely be its own thing.
