There are a surprising number of movies about Anastasia. All of them involve her surviving the massacre, losing her memory, and adding varying amounts of weirdness. The existence of four rip-offs of Don Bluth's Anastasia just goes to show how convincingly Disneyesque that movie is
Sliding Scale of Anastasia Movie Accuracy
From most historically-accurate to least historically-accurate
This is as historically-accurate as it gets without going all the way. It realistically depicts the aftermath of the revolution (for the most part), and manages to give a semi-believable reason for Anastasia to be alive, plus it has her at the right age. But of course, the movie still has to downplay the seriousness of the event by turning the Bolsheviks into a Goldfish Poop Gang, giving Anastasia an animal sidekick, and throwing in cartoony slapstick here and there. Also, throughout most of the movie, nothing happens.
Fox Animation Studios
With realistic movements, and at least some understanding of Russian history, this movie actually comes in second in terms of accuracy. However, Anastasia is depicted as being much younger during the revolution than she was in real life. The Dowager Empress gives up hope, when in reality, she never gave up. Anastasia gets the mandatory cute animal sidekick. There's a romance that never really happened. And, of course, Rasputin is depicted as an evil wizard with a talking bat, who started the revolution with evil magic, and came back from the dead as a magic lich who sends radioactive demon minions to do his bidding.
Yep, the one with the talking birds is the third most historically-accurate. Ignoring the bird sidekicks, it does have the Romonovs being killed (halfway through the movie), and it features the Bolsheviks as villains. But once again, Rasputin is an evil sorcerer, but this time, he's actually integral to the story. There's a romance that never really happened. And because it's Golden Films, what's left of the story is very watered-down to "protect" the children.
There's barely anything accurate here at all. The revolution happens because Rasputin made a deal with Baba Yaga, and the Romonovs were blown up instead of how they actually died. Also, Rasputin is an evil wizard again, but this time, he uses bombs to get the job done. On top of that, this being Dingo Pictures, there are all kinds of random things thrown in haphazardly.
Here's what they got right: the Romonovs died. Everything else is wrong. Cheka was not a person, it was the name of the secret police. There was no Prince Paul, nor anyone disguised as Prince Paul. Once again, the Dowager Empress never gave up hope. The thing with the song was dumb. There was no romance between Anastasia and some guy named Vladimir. Anastasia also was not betrothed to anyone. But, the worst part of the movie is what they did to the Romonovs. I can assure you that the Romonovs never transferred their souls into musical instruments after they died. Also, there were two more Romonov daughters.
Fox Animation Studios
Nothing about this movie makes sense if you've seen Don Bluth's Anastasia. In terms of historical accuracy... there is none. It's a straight-up fairy tale. It wouldn't even be mentioned here if it weren't connected to an actual Anastasia movie.