I mean, fall, for Americans, is a period within autumn in which the leaves of most trees fall.. Not the whole season. Here's some sauce from the world's worst English dictionary.

Edit: Excerpts:

A number of writers used the phrase "the fall of the leaves," which then came to be associated with the season. This phrase was shortened in the 1600s to fall.

And quoted from a poet, in turn their friend:

"In North America the season in which this [the fall of the leaf] takes place, derives its name from that circumstance, and instead of autumn is universally called the fall."