The performer needs to be an outgoing person who wants to make people laugh. Some people have this gift naturally. They are the ones who are surrounded by a crowd of friends and are delighted to tell jokes and make their friends laugh. But if you are not like this, don't despair. Sometimes it's the quiet ones who shine onstage. They find that another part of their personality seems to step forward and take over in a way they just don't feel comfortable doing in real life.
A writer of humor is likely to be a person who would just hate to have everyone looking at him on the stage. It would be his worst nightmare. He likes to write when the idea hits and not be confined to a time-slot of five minutes at 9pm or earlier for his delivery. He may or may not love to tell funny jokes to his many (or few) friends, but he does love to write them. He sees humor in every situation - even when the cat throws up on the new clothing on Christmas day.
The performer may not have a single humorous thought - ever. But he may be absolutely brilliant at performing someone else's humorous writing. He has an expressive face or expression that makes people laugh even if he only says one word. Or he may be the master of the straight face. He may be able to deliver his routine without any expression on his face at all and have people rolling in the aisles with laughter. He has that gift that when he walks onstage people start to laugh. He could read out a menu and make it seem funny.
So which one do you want to be? Or perhaps, more to the point, which one are you? The skills for each are sometimes inherent - either you have them or you don't. That's not to say you couldn't learn to be a comedian or a writer, but if you find it hard to see humor in everyday situations, then you might find being a comic writer rather difficult.