In the U.S. we use the term Japanese-American to refer to Americans of Japanese descent. The Japanese use the terms nisei and sansei to denote second- and third-generation Japanese. Then there is hafu to describe those who are "half Japanese" and half something else (such as mermaid?).
But I've never heard of an American-Japanese in Japan or a similar term to describe foreigners who have emmigrated here who appear to be gaijin but live like and act Japanese.
This group I refer to as Gaijin-Japanese. We eat Japanese food, we speak Japanese, we may even hold positions within the community other than "token gaijin." We've given up gaijin privileges such as talking in loud voices, wearing jeans to work and blowing our noses in public.