It's a subtle difference, but I would say that (1) is equivalent to"She was angry when she left the party," and (2) indicates that she left the party "in an angry manner" (maybe she slammed the door on her way out). Probably both would occur at the same time, but sentence (1) describes her mental state and sentence (2) describes the manner of her exit.
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(1) "angry" is a noun and states what type of mood or state she was in when she left.
(2) "angrily" is an adverb which gives us information on the verb. How did she leave the party? She angrily left the party.
(1) Refers to her state.
(2) Refers to the way she left.