"In American English, college is just a synonym for university."
Well, not exactly. Typically, a university has a teaching and a research mission with a graduate school and usually consist of a collection of colleges that award graduate and undergraduate degrees.
A college is typically a part of a university or is a stand-alone institution that awards undergraduate degrees and may, but probably does not, have a major research mission.
College and University are often seen as synonymous, but in reality they are most often very different entities.
For example, I am currently employed in the "College" of Education at Eastern Kentucky "University". In August, I will be employed in the "Department" of Education at Georgetown "College"....Georgetown College and Georgetown University are two distinct and different institutions.
Steve