(ごかい) A misunderstanding- often used about situations (a la TV sitcoms) or when you misread someone’s feelings.
(かんちがい) Like the related term 誤解 (misunderstanding), but 勘違い is a little smaller. If I’m reading and confuse one kanji with a similar looking kanji, that’s 勘違い. But if I see my fiancée with her cousin from out of town, and assume she’s having an affair and punch the guy, that’s 誤解.