“Getting pissed” for a Brit means “drunk”. “Pissed off” meaning “angry” is an American expression.
The word ‘pissed’ in isolation means drunk. When combined with the word ‘off’ as in ‘Pissed Off’, this also means ‘angry’ in Britspeak (although in another context, this phrase can also mean that the person being talked about has left and gone somewhere else)... Context is important here ;)