well hierarchically speaking:
1) a joke is told. Humour can be situational and non-intentional, or it can be told.
2) something that makes people laugh. As discussed elsewhere if they don't laugh - they don't consider it a joke - that's their problem.
3) There has to be a dichotomy in the listeners mind. Ambiguity, surprise, realisation after obfuscation. If you have heard it before it often is not nearly as funny. If the delivery gives away the surprise it is usually considered weak.
3) then you can start to subdivide the forms of humour. Situational, pun/paronomasia, shaggy dog, irony and probably more if you cut the cake thinner. I have heard Ken Dodd (who is fanatical about studying the nature of humour) cites 5 or was it 7 types of joke?

Roman joke
Ant walks up an elephants leg, and says "I hope you don't mind me walking up your leg?" The elephant says "I didn't notice you arrive, I shall not notice you leave". Now I would give that 90% irony, 10% situational.

Another Roman joke
"Man walks into a barber's and the barber says "How would you like your hair cut --- Sir?" "In silence" came the reply. Situational? hard to categorise.

young female at a Whitehouse dinner to Calvin Coolidge (famed for being a man of few words) "I have a bet on that I can get you to say more than 3 words" - "You lose" say he! Situational? Snopes on that

Having said that - I will always fall about laughing at Gerrard Hoffnung's Debate at the Oxford Union - lets call it "the Pile of Bricks", he may have called it something else which would give away the punchline (the final one that is). No matter how many times I have heard it, there is something in his delivery that he even pauses for us to predict the next event and we still laugh
It is - just - well - IT'S FUNNY!