For most people, this represents the differences between crocodiles and alligators quite well, but for those who want to know the real difference, here’s the official version according to live science:

• Snout shape: Alligators have wider, U-shaped snouts, while crocodile front ends are more pointed and V-shaped.
• Toothy grin: When their snouts are shut, crocodiles look like they’re flashing a toothy grin, as the fourth tooth on each side of the lower jaw sticks up over the upper lip. For alligators, the upper jaw is wider than the lower one, so when they close their mouths, all their teeth are hidden.
• Home base: Crocodiles tend to live in saltwater habitats, while alligators hang out in freshwater marshes and lakes.

[Source: John Atkinson – Wrong Hands]