1. A sarcastic way of saying "I don't care."
2. An ironic form of saying "I don't care."
The differences are how they are conveyed in a particular situation, or who it is conveyed to.
Sarcasm : Person 1. "I can deadlift 430lbs" Person 2. "Care"
Irony/Sarcasm : Friend 1. "Guys, i just looked, and im down 75lbs now!" Friend 2. "Care" *all friends laugh*
Irony : Friend 1. "Yeah bro, i dropped 32 kills in warzone yest-" Person 1. "Warzone?! I love that game, i win every single game i play." Friend 2. "Care" *Friends laugh* Person 1. *confused* "Thanks, we should play some time!"