Humour goes by many names — parody, satire, farce, and others.
Wordplay is an example. Oxford tells us wordplay is a means of achieving humorous effect by using or playing with words. This effect might be dubbed satire, irony, or even drama.
Wordplay and play on words are not identical. Wordplay is playing around “with” words, including making puns. A pun is itself a play “on” words and is defined as, “using a word to suggest more than one meaning.”
A double entendre is more or less the same thing. Translated, this French term means, “double sense; double meaning.” It’s something that can be understood in two ways with one meaning often bearing a coarse sexual connotation.
Wit is related to all of the above. When this word entered Old English, probably from Old Norse, it referred to the mind, to thinking and wisdom. In current usage, it retains that relationship and is defined as, “quickness of mind; ability in pointed humour.”
Witticism, coined by English poet, John Dryden (1631-1700), refers to a brief remark or retort often uttered during argument. Close, but not the same, is wisecrack, U.S. slang meaning unrehearsed quip often verging on insult.
Much humour tends toward the physical rather than to the intellect. Farce, for example, is unsubtle and is set up to evoke laughter. We borrowed this term from the French, farce (stuffing). Its ultimate source is the Latin, farcine (to stuff). In 13th-century English, farce referred to words inserted into passages of liturgy, maybe a French phrase added to the Latin text, usually to clarify the message. Today, farce is exaggeration built on coincidence, mistaken identity, misunderstanding, and embarrassment. Although often acted, farce’s primary expression is the written word.
Slapstick is loud, boisterous farce. Burlesque is comedy that satirizes via exaggeration. Parody is mocking imitation, often using exaggeration for emphasis. Burlesque, caricature, and parody are different in presentation. Actions are burlesqued. Form and features are caricatured. Manner of speaking is parodied.
Satire and irony are more subtle than burlesque, parody and farce. Satire is a written attack hinting at weaknesses or abuses in society or government. Irony, often sarcastic, is a way of implying the opposite of what is said.
A joke is a funny story. A jest is something said or done to evoke amusement. A gag is a practical joke, remark or hoax.
A Joe Miller is a worn-out joke, a chestnut. This early 19th-century term came from the name of an actual English comedian (1684-1738). Following Miller’s death, a joke book, Joe Miller’s Jests, was compiled by John Mottley (1692-1750), an English writer.
A shaggy dog story is a long, involved, pointless story. Whimsy, probably from “whim,” is an odd or capricious idea. Whimsy is usually quaint, fanciful or odd — never ordinary. A buffoon is a clown, jester, or one who makes coarse jokes.
Let’s end with a Joe Miller that also puns:
“I hear the admiral married a girl who ran away from him.”
“Yes. He took her for a mate, but she was a skipper.”