"Thank you, bye!"
I thought "pa" was predominantly used by women. "cześć" is more unisex.
I would say that "pa" is more infantile/caressing/warm (I am not these are the best adjectives to describe it). Therefore you would typically use it when talking to someone with whom you have a closer relationship (closer friends, family; I don't think it is used predominantly by women). Another example would be talking to children or even babies: "pa pa!". "Cześć" is definitely more universal (although still informal, e.g. you wouldn't use "cześć" with a vendor in a grocery store -- you would say "do widzenia").
Note also that "cześć" can be used at the beginning ("hi/hello") and the end ("bye") of a conversation; "pa" - only at the end.