Inside the US, we don't refer to ourselves as "American", we seem to go by whatever the hell our descent was, but outside of the US we refer to ourselves as "American".
Is America the only country that does this?
Also, on another note: To all you who are not native English speakers: When you buy a videogame, do you play it in English or your native language?
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In the US, if you call yourself "American" you imply a sort of patriotism that not all want to express. If someone asks, I'll say I'm American, because anything else would be a joke. (Yeah, my ancestors were Finnish, but I mean, c'mon. I don't know a thing about Finland. The only Finnish in me is in my long blond hair and high hair line.)