Costumes are outfits that Kat wore during specific side missions and story missions in Gravity Rush and Gravity Rush 2, when it thereafter became wearable anytime. Her outfits can only be changed at her Pipe House in Gravity Rush and via her camera in Gravity Rush 2.
Minor details aside, the "White Kat" costume (Pre-Order exclusive) in Gravity Rush 2 is actually based on one of Kat's early designs. Her outfit's color was the only major change between said early design and her final one.
Both variants of the School Uniform are obtained from missions given by Newt in each game.
The "Super Star" and "Dark Angel" costumes are the only ones that change Kat's hair color; going from blonde to pale purple and black, respectively. How this happens is unclear.
Kat's "School girl" outfit is the only one from the first game that doesn't appear outside of Gravity Rush where Kat is a guest character.
The "Maid" Outfit is available in Everybody's Golf 6, while her "Cat Suit" and "Military Uniform" are both featured in PlayStation All-Stars Battle Royale, as DLC in both games.
The outfit Kat wears as Queen Alua, as well as the "Mining Suit", are the only costumes that cannot be obtained outside of the episode in which they appeared.