Americans often use the terms "school," "college," and "university" in a very careless and confusing way: e.g., many will speak of someone being "in school" when they mean that the person is studying at a college or a university. However, in the US, "high school" signifies the last four grades of the secondary education that everyone gets; "college" signifies post-secondary education, for those aged 18 and older, though properly it excludes post-graduate education (i.e., education for a degree subsequent to a bachelor's degree). The term "college" may also be applied to a division of a university, usually the undergraduate liberal-arts division, but sometimes also to the individual graduate and professional schools.
In the UK, all of these words except "university" are used quite differently. I don't know if the Britons even use the term "high school," and I am pretty sure that they don't use the phrase "in college," at least not with the meaning that it has in the US. I have heard the term "college" applied both to English public schools, such as Eton College, and to the residential institutions that make up the universities of Oxford and Cambridge.