When asked for his ethnic group, a White American might just say that he is American. Others might say Mexican-American, Chinese-American, or black American.
AmericanAMER'ICAN, adjective Pertaining to America.
AMER'ICAN, noun A native of America; originally applied to the aboriginals, or copper-colored races, found here by the Europeans; but now applied to the descendants of Europeans born in America.
The name American must always exalt the pride of patriotism. - Washington
I occasionally hear people say that America was founded on a idea, or that anyone believing in certain ideals is an American. That was not the usage in 1828, according to this dictionary.
Note also that the dictionary makes no reference to citizenship.
If a non-Japanese person becomes a citizen in Japan, then he is still not considered Japanese. I am told that there are Koreans who have lived in Japan for generations, but they are still not considered Japanese.