To let out a chuckle or giggle is to laugh: people laugh when something is funny.
To chortle, cackle, guffaw, or titter is to laugh. The job of a comedian is to make people laugh. Often people laugh at things that aren't supposed to be funny, and people also laugh to be polite. If something is silly, you can say "That's a laugh!" If you had fun at a party, you can say "Thanks for the laughs." Everybody's laugh sounds a little different. It would be a shame if your laugh sounded like Elmer Fudd.