> "American" on the other hand is purely a citizenship ...

This may be how you perceive or feel about it, and of course you're not alone, but many other Americans feel differently. Those of us with Colonial ancestors maintained much the same culture and mores for generations; it's evident in the manners and the literature; it's something distinct that we certainly feel as close to an ethnicity. Granted, we comprise multiple European heritages, but those heritages did not define any of us after a few generations. The concept I am trying to outline her is also a very old one: e.g., first Speaker of the House Frederick Muhlenberg, referring to some of his own constituents, said, "The faster the Germans become Americans, the better it will be."

There has always been some concept of a process by which people can become American and join in that culture through assimilation and integration.

I've had ancestors in North America since 1650, including a vice president and a union admiral, but I also have friends whose parents arrived from Somalia or Vietnam in the eighties and nineties who grew up in largely the same cultural soup I did, speak with the same accent, have the same humor, drink the same beer and eat the same food. Some have served in the US military. In my eyes, they're just as American as I am.