The terms are used interchangeably in the US, partly because college is a shorter word than university but also because technically, when referring to an undergraduate education, college is correct.
Historically, in the US, undergrad studies were undertaken in the college part of a university (i.e. the undergraduate schools). The distinction between college and university is that one awards undergrad degrees only and one awards both undergrad and postgrad degrees. Liberal arts colleges award undergrad degrees only. They are not second rate third level institutions because of this - many are extremely selective and have endowments on a par with the leading Ivies.
Some universities preserve the historical distinction between undergrad and post grad education - examples are the University of Chicago, where undergrads apply to and graduate from The College, Georgetown University (College of Arts and Sciences), Harvard College - there are many, many more. Colleges include leading institutions such as Amherst, Williams, Barnard, and there are many more.
Within each university or college there are schools - School of Liberal Arts and Sciences, University of Illinois, for example. Some universities have both colleges and schools - the University of Washington has a School of Computer Science and Engineering and a College of Engineering. For some universities, you need to apply to a particular school within the university, not the university in general.