In the United States, this is a very complicated question. Every school has its own terminology and the answers are not exactly the same everywhere. The quickest answer is that "college" and "university" are both "higher education." Typically, A "college" is a four-year school which you enter at about age 18 after graduating from "high school." During those four years you are an "undergraduate." Then you graduate with a "bachelor's degree." A "university" is an institution of higher education that includes a "college" and also includes other specialized schools, like a law school, a medical school, and other "graduate schools" that follow college. The terminology comes in part from the traditions of medieval universities like Oxford and Cambridge, in which the university was a collection of colleges but I won't try to explain that. Let´s start with a simple and "typical" situation. Harvard University has many specialized "schools." Most of them are called "schools." The formal names of some of them include "Harvard Business School," "Harvard Medical School," "Harvard Dental School," "Harvard Divinity School," "Harvard Law School," etc. They are Harvard's "graduate schools." One of those schools is named "Harvard College." That is Harvard's "undergraduate school." So, a student might (dream of!) 1) graduating from high school at age 18; 2) "going to college" at Harvard College, spending four years as an undergraduate; 3) "majoring in" economics, i.e. taking a program with many courses in economics; 4) graduating at age 22 with the degree of Bachelor of Science in Economics. They are now a "college graduate" with a "bachelor's degree." They are now ready, if they wish, to enter a "graduate school" at Harvard or another university, possibly a business school where they would continue to get an "advanced degree" like an MBA.

Here are some additional details that apply to the United States. 1) We never use the word "college" to refer to secondary-level education. (The US being what it is, never say "never," but I can't think of an exception offhand). 2) A "university" is normally expected to have more than one "school," including an undergraduate "college" and advanced graduate schools, but this rule is sometimes broken. 3) After high school, we "go to college." We don't use the phrase "go to university" as the British do, although it would be understood. We don't use the abbreviation "uni." 4) There are some schools that are simply colleges and don't offer advanced degrees. There are some famous, excellent, prestigious "small liberal arts colleges." 5) Very, very confusingly, there are at least two universities which--for reasons of history and tradition--choose to call themselves "colleges:" Dartmouth College, and the College of William and Mary. To repeat, these are full-scale universities. 6) There are institutions called "community college" and other "two-year colleges," that follow high school. They award degrees that are lower than the bachelor's, sometimes "associate's degrees". You may hear the term "four-year college" used to make the distinction clear. For example, at a job interview you might be asked if you have attended a "four-year college." 7) Universities typically have one undergraduate college, but there are exceptions. The great medieval universities of Oxford and Cambridge in England have multiple colleges--I think graduates don't say "I went to Oxford," they say "I went to Balliol" or "Keble" or whatever. Similarly, a few US universities--Yale University is an example--have multiple undergraduate colleges, although graduates just say "I went to Yale."

As you've probably realised by now, Arianna, it all depends on the country which the speaker is referring to. Different English-speaking countries have different educational systems and use the same terms differently. In fact, there's hardly a single education-related term in English which British and American people use in exactly the same way. Here are just a few words which mean different things on different sides of the Atlantic : school, class, college, faculty, term, grade, professor, tuition, graduation, revise. It's all about context. A very rough-and-ready answer to your question is this: if the native speaker is from the US, probably yes. If the speaker is from another country, probably no.

In New Zealand, a college is either a name of a secondary school, or an internal subdivision of a university - such as the college of Engineering, or the college of Science. It is not a synonym for a University.

Part Two Of course, it's much more complicated than that, and many thanks to Dan for his very comprehensive explanation about the US system. And if Arianna doesn't mind this turning into more of a Discussion thread, I have a couple of comments on Dan's answer. 2) Would I be right in thinking that a US student would only say 'I'm at college' for the first four years of higher education? Let's say that someone spends, say, six/seven years at the same university. Would they refer to their undergraduate years there as being 'at college' and then their subsequent years at its Law School as being 'at grad school' (?) rather than 'college'? 7) May I correct you on that point? We do say 'I went to Oxford' or 'I went to Cambridge'. We'd only specify the college if it were clear from the outset which university we were talking about. For example, a group of Oxford graduates might refer to their colleges in a conversation amongst themselves. Without specifying which university you're talking about, references to colleges can be very confusing. Combined, Oxford and Cambridge have in the region of 80 colleges, many of which are not well-known in the 'outside world'. Even more confusingly, there are also some duplicates. Both have a Corpus Christi, a St John's, a Trinity, a Jesus and a Wolfson; Oxford has Magdalen while Cambridge has Magdalene (neither pronounced as you'd expect!); Oxford has Queen's while Cambridge has Queens' (it's all in the punctuation!). Even with most well-known of colleges, the reference isn't obvious. For instance, if someone were to say, out of the blue, 'I went to Clare' or 'I went to Jesus (!)', this would confuse the listener. Corpus Christ Christi could be a church or a hospital, and even King's College could be King's College London (also a collegiate university) or else any one of any number of modest secondary schools up and down the country.