There are differences in usage. For example, you would say "fall semester" (approx. Sept. to Dec.), never "autumn semester." One of the characteristics of autumn/fall is the leaves turning color and falling from trees. Such leaves would be called "autumn leaves," rarely "fall leaves."
If you've been out of college and are going back in Sept., you would say: I'm going back to school "
Hi, Anon, I agree with you that the usages you cite are traditional. I'd take issue with the last one, however. I prefer "Fall is my favorite time of the year." I think both are common.
"Fall is my favorite time of the year." is entirely correct, from a purely grammatical point of view, and should be completely equivalent to "Autumn is my favorite time of the year.", but there is a problem with it in that the word "fall" has many negative connotations. "Autumn is my favorite time of the year." has no such negative connotations and therefore sounds better.