en.wikipedia.org/wiki/Stand-up_comedy
To be fair, stand-up comic is also in that list, so... whatever suits you.
"A comic says funny things; a comedian says things funny" - Ed Wynn
If the material is funny you're talking about a comic, if the person was funny when they said it they're a comedian.
Jim Gaffigan is a comedian because he will say stupid-not funny things (Bacon... bacon... bacon...) and people laugh because of how he said it.
George Carlin is mostly a Comic because his stories are easy to relate to and funny, while he
often isn't saying things in a funny way.