I was watching Pulp Fiction tonite and I suddenly realized that Uma's character makes reference to her failed pilot, Fox Force Five, and her character's prowess with knives. It made me think of her role in Kill Bill, and the Deadly Viper Assassination Squad. And since they're both Tarantino movies, and he has stated in the past that some of his characters are related, I started to wonder if Kill Bill could be considered a movie that exists within the Pulp Fiction universe, or if they're related in some way.
In my opinion, the answer is "certainly not". The Pulp fiction wiki for Mia & the Kill Bill wiki for Beatrix Kiddo state no connection at all. In spite of that there is large difference in the two characters as well. Mia Wallace is a cocaine addict whereas there is no indication anywhere that Beatrix uses any kind of drugs. The character that Mia Wallace played in that failed pilot was an expert with knives not Mia Wallace herself. Also going by the characters' ages Mia Wallace is around 10 years younger than Beatrix kiddo. Kiddo was a trained fighter, but Mia is much younger and the context that you are trying to indicate is that Mia was already trained at that time and had left the Viper assassination squad, but this seems highly unlikely.
Adding more info wrt Ben Plont's comment : Fox Force 5 is fictional in Pulp Fiction. Fox Force 5 does not actually exist while Pulp Fiction is taking place. Relating these two would be like "there is a fictional show that is in the Pulp Fiction universe and then later in that same universe this story became true, meaning Fox Force 5 became an actual thing and the fictional character that Mia was playing became an actual character", Come on!! that wouldn't make sense. What I think is that Tarantino had this kind of idea (Fox Force 5) back in 1994 and which he used as a fictional TV show in Pulp Fiction and later developed that same idea into a full fledged movie as kill Bill. But Mia and Beatrix are definitely not the same girls.
In addition to the previous answer, I'd like to point you to this:
where it says:
The pilot, she [Uma Thurman] says, was about a hit squad comprised of five women, called Fox Force Five, who go around killing people and telling bad jokes. It actually did sound utterly awesome, like something Tarantino should make ...
... and he did. It's called Kill Bill.
So far, I am unaware of any official rejections to this, so, they may not be the same person, but in a way the same "character".
PS: Something else related just popped up: Kill Bill ending Q & U. What does that mean?
There are many theories on this. Tarantino said that a lot of his films can be watched by characters in other films. Because of this I think Kill Bill is a film set in the pulp fiction/Reservoir Dogs universe based on Mia Wallace’s failed TV show. This would explain all of the similarities between the two as well as it’s quirky style. I also think that Samuel L Jackson’s character in Kill Bill (I forgot his name) is actually Jules who’s doing one last job to leave like he wanted.