You have comedians who just do jokes, and they're called comics, not comedians. You have comedians that do bits - a person that has a lot of jokes that have a beginning, a middle and an end, but it's not a real story. And you have someone that does great stories, the one that blends those things together - that person is doing comedy.
There are many styles of standup, but the comedians I like are people like Dick Gregory and Richard Pryor. Because Richard Pryor told the truth. Chris Rock. I love Chris Rock. He's funny, but he's also poignant. He's not there just to make people laugh; he's there to make people wake up, too.