Jack Napier is a petty crime lord, a jack who wants to be king. But the king of this deck of Gotham City mobsters—Carl Grissom—sees Jack as more of a nine of diamonds, or maybe even a two of clubs: mostly useless and expendable.
A chess metaphor would be more apt than cards here, we think. Napier wants to be the pawn who makes it to the other side of the board and evolves into a stronger piece. After all, Jack thinks that:
JACK: He can't run this city without me.
Napier is cocky, over-confident, and full of himself. And when Grissom finds out that Napier wants to take over, he decides it's a good time for a game of Slap Jack. Okay, we're back to card metaphors now.
A Joker is wild card, and Napier's acid-borne alter-ego Joker makes it his mission to cause chaos in Gotham City. He sees art, beauty, and humor in death and destruction. He also fancies himself an artist instead of psychopathic murderer.
Perhaps because of his focus on appearances, Joker's targets are often beautiful women and models. He poisons cosmetics, and his first big crime ends up killing two models and three women at a beauty parlor. The fashion industry is often accused of being inhumane, and Joker's crimes manage to be even more misogynistic, leaving many dead women in his wake.
Before becoming Joker, one of Napier's goals is to have Grissom's girlfriend to himself. After becoming Joker, he uses Grissom's girlfriend's face as his canvas, tormenting her until she commits suicide. With her dead and disposed of, he sets his sights on Vicki Vale, telling his lackey:
JOKER: I'm about to get a new girl, Bobby. I'm of a mind to make some mooky.
Joker sees women more as objects either to manipulate their appearance or as trophies to be won. A lot of card games are played without a Joker in the deck, but they do need the queens. It's Joker who is expendable, not the women, so Batman makes it his mission to remove him from the game.
Full of Himself
Joker is greedy and vain, and he targets citizens of Gotham who possess the same vices. His cosmetics plot endangers the lives of anyone who purchases a product to look better. After Batman foils that plot, Joker drops money in the city to lure out its greedy citizens and gas them.
But Joker's own greed and vanity do him in. His greed leads him to being dropped into acid and becoming Joker. And Vicki exploits Joker's vanity in Gotham Cathedral, distracting him so that Batman can get the upper hand. Joker's so vain, he thinks Vicki is actually into him, saying:
JOKER: It's as though we were made for each other. Beauty and the Beast. Of course, if anyone else calls you "beast," I'll rip their lungs out.
Jack Napier was vain too. He tried to establish himself in the crime world with a silly catchphrase to utter every time he killed someone.
JOKER: Tell me something, my friend. You ever dance with the devil in the pale moonlight? […] I always ask that of all my prey. I just like the sound of it.
Repeating this phrase exposes him to Bruce Wayne as the killer of his parents, which makes Batman even more determined to bring Joker down to avenge his folks. Couldn't he have gone with someone more trite, like "Stick 'em up"?
Green with Envy
In addition to greed and vanity, Napier's biggest driving force is also his biggest weakness: envy. He envies Carl Grissom's position as kingpin, he covets his girlfriend "Sugar Bumps," and once Batman shows up on the scene, Napier envies him and his gadgets.
JOKER: Where does he get those wonderful toys?
When Grissom finds out about Joker's ambition, he sets him up to be killed by the police. That's when Batman accidentally drops Napier into a vat of acid, inadvertently birthing Napier's alter ego: Joker. As Joker, Napier wants more, more, more. He wants more money, more power, more fame, more women. Permanently unsatisfied, Joker keeps reaching and climbing until he literally falls off a building and dies.
If Joker had Batman's "wonderful toys" he may not have died at the end. Both Joker and Batman plummet from the roof of Gotham Cathedral, but Batman manages to save himself with his gadgets. Joker's laughing box does little to break his fall.
Anyone who says "laughter heals" hasn't tried to save themselves from a 100-story fall by chuckling.