pissed off vs annoyed

pissed off and annoyed both are adjectives.

Word	Noun	Adjective	Verb	Adverb
pissed off	No	Yes	No	No
annoyed	No	Yes	No	No

As adjectives, pissed off and annoyed are synonyms defined as:

Other synonyms of pissed off include irritated, miffed, nettled, peeved, pissed, riled, roiled, steamed, stung.

pissed off (adjective)	annoyed (adjective)
aroused to impatience or anger	aroused to impatience or anger
	troubled persistently especially with petty annoyances