There are many reasons why I think that all of the stories in the franchise (Murder House, Asylum, Coven, and Freak Show) are set in one, shared universe (that just has a lot of really messed up stuff happen). Below are my reasons why.
- There's no evidence against it.
- Pepper has appeared in two stories.
- Naomi Grossman (the actress who portrays Pepper) has even stated that the Pepper in Asylum is the same as the one in Freak Show.
- While one could argue that in Asylum, it is stated that Pepper lived with her sister, and not in a Freak Show, we are never told Pepper's story from her point-of-view, and since the Asylum was corrupt, it is possible they lied.
- Another possibility is that Pepper simply moved in with her sister in the ten years between Freak Show and Asylum.
- Just because some actors/actresses portray more than one character doesn't make the other characters non-existent. It simply means there is more than one person who looks similar.
- There are many references to Asylum in Freak Show.
- Timeline-wise, nothing has contradicted anything else.
- Example: The anti-Christ was born in Afterbirth, but we see that three years in the future he's still living a normal life (well, normal for a murderous three year old). While that scene would take place after Coven, it is not long enough to prove or deny if Witches had been announced as real or not.
This is just my personal thoughts on it. I choose to believe they are one universe, but I am interested in hearing everyone else's opinions on it.