Irish American (for example) is an ethnicity, unless you have (ok, or could have if you bothered to apply) two passports. Pretty much the rest of the world finds it weird that Americans generally report ethnicity when their nationality is what is being enquired. All the scots and irish people i know find it curious* when people who are clearly American try to tell them they are irish/scottish.
Not critisising, i figure ethnicity just has more relevance over there -- with the notable exception of a few cities, here it's just english, scottish, welsh, indian/pakistani, and a few others -- but it does come across a bit like you're trying to imply you're just visiting for a generation or ten, like you're trying to distance yourself.