The crocodalians include alligators, caimans, crocodiles, and gharials. Crocodalia splits aligator and crocodiles into different groups in crocodalia. The way to tell the difference between alligators and crocodiles is very simple. The main way I personally use is that the snout of crocodiles are more trianglular than alligators, and slligator snouts are wider. (Gharial's snouts look like striaght lines, and are very easy to tell about from that) Another way to tell is that crocodiles often have more teeth showing from the side of their mouth than alligators. In addition caimains are often smaller than alligators crocodiles and gharials.
Osteolaeminae, Crocodylius, Mesitops
Gavialis, Tomistoma
Caimaninae, Melanosuchus, Paleosuchus, Alligatorinae (Fun Fact: There are 2 species of alligator, the chinese and american.)