You are both. One is your nationality and the other is your heritage.
If you are born in another country and your parents are from that country and you move to America, then you're a citizen of that country. If you decide to become a citizen of America you have to go through a 5 year process. (3 years if you marry an American citizen, but you have to have been married for two years to prove that you're not married just for citizenship...so, in the end, they're both 5 year processes.)
If your parents are living in another country but are living in another country and you're born, then you can get a dual citizenship. I think that is up to your parents. I learned all this a year and a half ago, so this may be a little sketchy.