Fall is more American and Canadian usage, while Autumn is mainly used in UK.
Here I found also a short but rather explanatory article about the history of usage of the two words, I'll paste it here for ease of reference:
Changing colour to color can be blamed on American dictionary maker Noah Webster, but Fall for Autumn deserves another look.
Taking the vocabulary of Old English as a starting point, both Fall and Autumn as names for the season between summer and winter are late-comers. Fall derives from an Old English verb, but it wasn’t used as a noun to designate the season until the 16th century. This use most likely developed from the Middle English expression “fall of the leaf.” So what did Old English speakers call the season? Harvest.
The need for a new word arose from a population shift that made cities more important than farmland. From being a word for the season, harvest came to refer only to the agricultural event that occurs in that season.
Autumn as a word for the season came into common usage about the same time as Fall did. The English who settled the eastern American seaboard brought the word Fall with them from the homeland. The English who stayed home eventually adopted the word Autumn. Nowadays in England “Fall” sounds archaic and poetic, but in U.S. English “Autumn” has those connotations.