Here are some broad categories, according to Bob Mankoff.
“Roz Chast is a reality cartoonist. Her cartoons almost always derive from her emotional reactions to her life. You can indentify with a reality-based cartoon. Thinking, isn’t life like that, or that’s an experience I’ve had or even an insight into how the world works.”
“In fantasy cartoons there is no real connection with reality. The whole purpose of the cartoon is to get a laugh. Here is a Farley Katz cartoon that epitomizes that.”
“Another type of classification is dependent on how the caption interacts with the image in a cartoon. Some cartoons [like this one from Leo Cullum] are what I call very text-centric; the image quickly locates where the joke is happening but the caption itself would let you deduce that.”
“[A text-centric cartoon] is very different than a cartoon like this, by Frank Cotham, in which the image is absolutely essential.”