There really isn't much difference.
"Wit" suggests something intellectual and clever, and perhaps slightly cold. It's related to the word "wits" which is a rough synonym for "intelligence."
"Humor" suggests something warmer and more natural--a way of looking at the world, rather than a way of making verbal jokes that have a "point" to them.
When I am playing with my grandchildren I often display humor, but not wit.
You can express humor without words. Someone might do it with body language--by raising an eyebrow, by smiling in a certain place. "Wit" always involves the use of words.
The writer Mark Twain is often described as a "humorist." If you read one of his books, such as Tom Sawyer, it is full of humor rather than wit. There aren't very many jokes as such, or clever uses of language.