There is one more difference Bob didn't mention.

You can учить both (A) something and (D) something.
The difference is marked by the case. Accusative case means that you study/learn that. Dative case means you teach that. Note that another verb (преподавать + A) is usually used instead of учить+D.

Я учу русский язык = I learn Russian.
Я учу русскому языку = I teach Russian, but Я преподаю русский язык is much more commonly used.