Nothing.
See, that's my point.
Heh, I understand that but that isn't really relevant to this discussion.
If you had to objectively classify Americans based on their skin color or ethnicity, that's what you would call me - and you would call black people "African Americans", "Hispanic Americans/Latino Americans" etc.
White American is a less used term since White = majority of Americans; and it is inferred to be the case if there is not distinction made. It also isn't very useful as a term since it is a blanket term for European ethnic origin.
I'm just talking about census based objective stuff obviously, making a distinction in what kind of American you are in a social context is often debated and I'm not debating that at all (but you can probably inductively conclude my thoughts on that based on my responses so far anyway).