Elia, In the U. S. there is no such a thing as residence permit. I believe that is only in U.K. and other European countries. There is work permit or Employment Authorization Document, which allow one to work legally in the U.S. For residence it would be either a student visa, which allows one to reside in the country as a student (for a limited time); or it is the Green Card which grants permanent residence in the country. Aida N.

That would certainly be understood as a generic term. The official term in the US is "Permanent Residence" for the status and "Permanent Resident Card" ("Green Card") for the document. In the UK, the term is "Indefinite Leave to Remain", and I think it's just a stamp in your passport, although I'm not sure.