Less then what it means to be Chinese, as that encompasses a nationality and(/or?) ethnicity, while being being American is just nationality. I'd put the meaning a bit above ID'ing as "European" or "African" though. If someone says they're American you know they're talking explicitly about the U.S. and not other countries on the North or South American continents, unlike the European who could be from Norway, France, Sweden, etc.

Strictly though? Citizenship.