Ethnic heritage and identity is as complicated as this question, so realize that there may not be any one particular answer that covers all the bases. Great question to ask onesself though.
I teach an Ethnic Studies class to a largely bi-cultural school, almost 50% Latino, and what many of my students are surprised by each term is the how layered and complex the Latino experience in America. Tejanos, Chicanos, first generation immigrants, second generations, Spanish heritage, Catholic, you can almost lose count, just as you can with the white population and the varied origins and identities within it.
As I have heard it said and written by numerous students in class, being Chicano means figuring out what your heritage is, within a society that does not make that easy, and without the experience of another country to base that on. It means figuring out how to be an American without forsaking where their parents or grandparents came from. And it means learning about that heritage, in an educational system that doesn't always make that easy.