What is the word for a university student who has a job at university?

I have to produce a copy of my CV in English and I don't know how to properly describe the position.

When I was a Master student, I was employed by a professor at our department, for whom I did some software development, some research, and anything the researchers didn't want to do by themselves (yes I had to clean the coffee machine). I think that such positions are regulated by law (at least they are here) and have a special, generally recognized name. Only I don't know that name in English.

If there are regional differences, I will need an American English variant.

I think you are looking for research assistant. If you also did teaching, you were (also) a teaching assistant.

I agree with Cerberus that RA or TA are the terms most often used at universities for the position described. The only other word I can offer is intern. That's certainly someone who would clean out coffee pots and the like.