Pissed = drunk UK and also Angry
But Pissed = Angry American.
Pissed comes from the fact that a lot of alcohol make you want to constantly go to the toilet and often leads to a drunk person loosing control of the bladder functions. Often not caring where and how they have to relieve themselves in public. "he was really pissed last night"
You can tell from context which it is drunk or angry.