If someone was born and raised in Poland, for example, then went to the United States and lived there, they would be considered Polish American.
My story, however, is a bit more complicated. I was born in Chile and stayed there with my family until I moved out as a child. Then, I lived in Brazil until I was 13 and moved to the United States. When I was 17, my family and I moved to France. Am I just Chilean-French or something? Chilean?
If asked, I would just say « Je suis né au Chili mais je réside à France maintenant. »
I reckon “polish american” means something like “culturally polish, but living permanently in america”
Beyond that, does it really matter? Labels are just shortcuts to give other a broad overview. Tell people what ever you want. You can always add more details later if you get to know them better.