I don't think of myself as an American. I happen to have been born in the United States, and as such I am a U.S. citizen. As a result of my citizenship, it's very convenient to live in this country and there are many benefits to doing so. I might live in America, but I'm not emotionally attached to it. If it makes sense to move elsewhere, I won't have a problem doing it.
I grew up in Virginia, went to college in Massachusetts, and currently live in California. I don't think of myself as a Virginian. I don't think of myself as a Massachusettsian. I don't think of myself as a Californian. Of the three, I might have the most fond memories of Massachusetts, but that has a lot more to do with MIT than the state itself.
I was born on Earth. I grew up on Earth. I will likely never leave Earth. And yet, I don't think of myself as an Earthling or a Terran. I don't have a particular Earth-calling grounding me, but rather I just believe that in my lifetime it is unlikely that there will be any draw for leaving Earth that is worth the cost and risk. I don't claim to predict the future, and maybe the situation will change faster than I expect. That's fine. I can adjust.
I also happen to be a human. But more importantly, I am a person. What exactly defines a person is a difficult philosophical question. At the moment, all persons that I know of happen to be humans located on Earth. But I don't want to be united as Californians, Americans, Earthlings, or even as Humans. I want to live in a world where we are united as People.