In the United States the word ‘pissed’ has come to mean ‘annoyed’ – in the UK it means something very different, and there are a number of different variations. None of which are usually used in polite conversation, it’s not the sort of thing you’d say to your priest.
The word ‘piss’ is a colloquial term for urine, and the other variations are derived from this.
‘Pissed’ – is a bar-room term for drunk or intoxicated – “He’s too pissed to drive home.”
‘Pissed Off’ – is closest to the American term, meaning annoyed “I’m really pissed off about this.” or “you don’t want to piss him off.”
‘Taking a Piss’ – is to visit the toilet as opposed to –
‘Taking the Piss’ which means to mock or make fun of, and a ‘Piss Artist’ – is someone who ‘takes the piss’.
In our neck of the woods (S.E. Wales) we would call someone a ‘piss artist’ if they were always going out getting smashed (really drunk), a borderline alcoholic.