Where I live, we sometimes make a distinction: trash is what goes into, say your office or bedroom wastebasket, and garbage refers to uneaten food, empty meat wrappers, etc., that go into your kitchen garbage can.

The distinction being, as I understand it, that "garbage" refers to organic matter -- or more specifically to the kind of waste which, if left unattended over time, will develop distinct and unpleasant odors or rotting.