Yep. As far as I'm aware (and I could be wrong), a university is generally composed of a number of colleges - as in King's College, Cambridge - but there can be stand-alone colleges as well. In any case, students consider it "going to uni" no matter where they go.
But as I say, I could be wrong. And I can't be arsed to Google it.
This is basically correct.
Tertiary level education in the UK is primarily delivered by universities. Universities are characterised primarily by their ability to award their own degrees.
(Prior the early 1990s, the former polytechnics were not universities because they required another body (like a university, or a trade or professional standards body) to validate their degrees. Since then, they've been able to validate their own degrees, so have fully-fledged university status. Historically the older universities have had larger research departments than the newer ones, though this isn't set in stone).
Students at university generally commence their studies at age 18. However the legal requirement for schooling in this country ends at 16 (there are moves afoot to lift it to 18 soon). Many secondary schools, esp. in certain parts of the country no longer have provision for teaching between 16-18 (the old tradtional "Sixth Form" under the pre-1990s reforms), so that means a gap between 16 and 18 which has been increasing filled by Sixth Form Colleges. Many of these Colleges realised they could also make money by offering some tertiary level education too, so Further Education Colleges developed which can include some non-degree (or professional/technical/vocational) courses too. These were often the kind of things that Polys might have offered in the old days (and many still do) before they gained university status and could focus on university degrees.
The Oxbridge colleges are something slightly different - financially quasi-autonomous teaching and living units within Oxbridge. They do have a similarity with all colleges though, in that they cannot give out degrees themselves, but rely on the wider university validating the degree. Using myself as an example, I studied at Lincoln College, but my degree is from Oxford University, not Lincoln.
So, in brief (and simplified from the above), in the UK, the traditional terminology:
University: can award its own degree. What the USA would call "college".
College: requires a university to validate any degrees ii offers
6th Form College: focuses on 16-18 teaching
Further Education College: can include some 16-18 teaching, but also includes tertiary post-18 education though limited in what it can validate for itself. Sort of similar the USA's community college concept.
