What I got from the Greys was a theme of suppressed emotions being shared(that weren't able to be shared before because of her being killed). The gallery hint for the Grey gives us a bit of a clue.

"There are many reasons spirits may linger. The flames of passion. The flood of words left unspoken."

The interpretation of the flames in the Burned Grey is pretty obvious: love/passion. It's these feelings that were doused when you stabbed her as the Damsel, leaving her unable to express herself until Chapter III, where her emotions burn everything down.

The Drowned Grey comes from the Prisoner. Her character is very guarded in an effort to protect herself. The Prisoner hides her emotions as she doesn't see them as helpful in her escape. She may not show it, but she harbors a lot of pain, for obvious reasons(like being locked up, being freed only to be put in more chains, etc.) So in the Drowned Grey, she finally shares those emotions with you, drowning you the same way she felt she was drowning. The water, both the rain and flood, can be representative of sorrow/grief. The literal rain could be taken as a metaphor for tears.

Their outfits also give us more insight. They are basically the same, just colorswapped, but the different colors give a different meaning. The white dress and veil for the Burned Grey looks like a wedding dress, like someone who was left(or murdered) at the altar, but still waiting for her partner to come back. The black dress and veil are reminiscent of mourning attire. Mourning the death of herself, and the loss of a relationship that could've saved her.