Joke, jest, jape, quip, witticism, wisecrack, crack, gag are comparable when they mean a remark, story, or action intended to evoke laughter.
Joke, when applied to a story or remark, suggests something designed to promote good humor and especially an anecdote with a humorous twist at the end; when applied to an action, it often signifies a practical joke, usually suggesting a fooling or deceiving of someone at his expense, generally though not necessarily good humored in intent.
Jest may connote raillery or ridicule but more generally suggests humor that is light and sportive.
Jape is identical with jest or joke.
Quip suggests a quick, neatly turned, witty remark.
Witticism, wisecrack, and crack all apply to a clever or witty, especially a biting or sarcastic, remark, generally serving as a retort.
Gag, which in this relation basically signifies an interpolated joke or laugh-provoking piece of business, more generally applies to a remark, story, or piece of business considered funny, especially one written into a theatrical, movie, radio, or television script.
Sometimes the word has extended its meaning to signify a trick whether funny or not but usually one considered foolish.