In British English to tick someone off means to tell them off. For example: The boss gave Steve a real ticking off for being late for work twice this week. To piss someone off means to make someone angry/annoyed.

I would add that "piss" is widely considered to be vulgar, or at best slightly crude. "Ticked me off" is still informal, but it is more generally acceptable than "piss." Either of these should be avoided whenever strict formality is desired. I think it is true that to be "pissed off" communicates a stronger anger than merely "ticked off," but the severity of the description depends to on who you are talking to.

"Pissing someone off" is more serious than "ticking someone off". Ticking someone off would be to annoy someone or make them angry or upset, but not to the point where they show an excessive amount of anger. If you make someone mad to the point that they start yelling or turn red or remember your affront for several days, then you would probably say that you "pissed them off." But there is some overlap between the two.