We use these terms loosely, though. In his recently published Autobiography, for instance, Mark Twain approaches his story by talking “only about the thing which interests you for the moment”—and is therefore more free-ranging than you would expect from a strict autobiography. “Autobiography” in this case most likely refers to the completeness of the work.
On the other hand—most common, everyday memoir writers (that’s you and me, the non-celebrities) say we’re writing memoir, but most of us are probably writing autobiography. Why? Because autobiography is simpler for the unpracticed writer. The structure is already in place: you start with birth, you end with where you are now.
Memoir might require a more skill—more time, more editing—to achieve the desired effect. It might also be more literary as thematic elements are explored and structure may not be a straight, A to Z shot.
Either way is a perfectly legitimate way to tell your story. The main thing is to get it told.