Faith was a ma...*spoiler theory*
Faith seems to have been a manipulator all along?
From looking at the pictures in-game,we know that Nerissa and Faith had a fight shortly before one of them died. I guess that's the moment when they somehow exchanged identities.
The Faith we see at EP 1 who says Bigby is not bad, seems to be the real one, since she uses the same phrases.
At that point I think Faith already knew she had messed up somehow, and that it was a matter of time before Georgie or Crooked Man found out she was trying to betray them.
Then it seems that sometime after that, Faith somehow convinces Nerissa to "trade" places with her. I assume that is happening in the photo where they're arguing. She probably asked her to cover for her or something, using the beating Woodie gave her as an excuse for being unable to work. Nerissa must have gotten upset for having to cover for her, but still agrees to do it for Faith and take her appearance to meet whatever client is next.
It makes sense that Faith could have asked for Nerissa to cover for her, didn't she do the same thing with Lilly, asking her to glamour as Snow and go see her other client , Crane? She probably just wanted to get them both out of the way for a moment.
They trade places, and fake Faith [real Nerissa] takes the bait and goes out to "cover" for the real Faith while mimicking her appearance. In the meantime, while fake Faith is out, the real Faith,now glamoured as Nerissa, rats her out to Georgie about their plan, pinning most of it on fake Faith, I'd assume.
And then when an unknowing fake Faith comes back from her job,and George kills her, thinking she was the real one. After that, having saved herself, the real Faith ,with Nerissa's appearance, takes fake Faith's head and places it on Bigby's doorstep, hoping that he could follow the lead , and take Crooked Man out and finally free her from him.
To me it seems that the real Faith did something really selfish to keep herself alive, at the cost of a friend's life. She seems to have planted evidence on her true Faith self as soon as she realized she was gonna get caught, and then asked an unknowing friend to take her appearance as favor to cover for a client. Then she backstabs her friend by taking her appearance and ratting her "fake self" out, letting her take the punishment in her stead. It seems her main priority was to save herself.
It's just like Buffkin said, it's in Faith's nature as fable to disguise herself and trick others in order to save her own skin.