In the US, we colloquially 'go to college'. College refers to higher education in general.

Then, in more academic terms, A university is a larger place of higher ed made up of schools and colleges. You also have liberal arts colleges that do not have these colleges/schools. We also have two-year community colleges that may be more similar to vocational schools or FE colleges in the UK.

Then we get to the level of fun: Boston College is actually a university. :-)

Source: I lived overseas and told people I attended _____ College, which caused them to cross-examine me about whether I have a 4-year degree because in their country people go to university/uni and college is something else. Different places, different terminology.