Both colleges and universities, in America, are education after high school (grade 12) and grant degrees: associate degrees (a 2-year program), bachelors degrees (a 4- or 5-year program) and masters and doctoral degrees (post-bachelors). (Trade colleges that don't offer a full 2-year associate degree program might offer a certificate instead.) Completing your first 12 years of education earns you your high school diploma. When someone asks you for your degree(s) in America, they want to know all the schooling you've completed after high school, with your highest university degree earned being the most important one. I'm sure you gave them the one they were looking for!

It's amazing how different the systems are. I know I would be completely lost if I had to write a German character's education!