What's the difference between an alligator and a crocodile?
In general, our advice would be to look at the sign or plaque in the zoo where you see the animal in question. If you see either and you're not in the zoo, you will probably want to run very quickly in the opposite direction and worry about its species later.
More seriously, while there are a number of different alligator and crocodile species, crocodiles usually have narrower, pointier snouts than alligators. When their mouths are closed, you can see some of the crocodile's lower teeth, but not the alligator's. And alligators usually stay out of salt water; crocodiles don't.