Some people use the term "college" instead of "university". Are they referring to a different type of university?
The difference between college and university is everything or nothing, depending on where you are in the world. There are a number of threads on the matter at EL&U, for example “In college” versus “at college” versus “at university”, “When I was in college…” Do you really mean college? Or university? and University vs college vs academy vs institute vs community college.
In different countries, they may refer to different types of institutions or different levels of education, or may be alternative names for the same type of institution or level of education.
University is reasonably universal in referring to a postsecondary institution which grants academic degrees in a diversity of subjects. College, on the other hand is considerably more diverse in its usage. In the U.S. alone, an institution called a college may be a secondary school, a two-year tertiary institution, a four-year undergraduate institution, a unit within a university (whether academic or physical/architectural), or a university itself— or, the common name for tertiary education in general, or a building or campus.
So, the answer truly depends entirely on context.
In the UK, "college" generally refers to a place of further education. That is, institutions of learning or training that you can go to after compulsory secondary education, but distinct from universities which are classed as higher education.
A further education college can be somewhere that offers vocational qualifications needed for a particular job or trade. They may offer more specialist or technical fields than are available at secondary education, e.g. an agricultural or technical college. They can also offer adult (post school-leaver) education for people who want to brush up on their skills, perhaps learn a new language, or take a course in a subject that wasn't available when they were at school. Or they can offer a means for those who need to obtain - or improve on - a qualification that they failed to get a satisfactory grade in, when they were in secondary school. Not all secondary schools in the UK offer A-level qualifications ("Advanced Level" or "Advanced Higher" in Scotland). In this case, school-leavers can attend a Sixth Form College to study for A-levels.
A UK further education (college) can be used as an alternative to higher education (university) for those who don't need to study for a graduate degree, don't wish to go that far, or don't currently have the required qualifications to get into university. It can also be used as a stepping stone to obtain an intermediate qualification, as a means of getting into university.
"College" can also be used to refer to a sub-division of a university in the UK (usually in the older, more prestigious institutions), although "school", "department", or "faculty" are more commonly used in this sense.
Sideline note: Sixth Form refers to the old school year numbering over here where the first year at secondary school was year 1 (1st Form), 5th year was the end of compulsory education and 6th Form (years 6-7, lower sixth and upper sixth) were optional advanced secondary education (usually as a precursor for going to university after.) The numbering system has changed since I was at school, as have the number of years of compulsory education.
In the US, "university" has a slight connotation of a higher-prestige institution than a "college". This connotation is not always respected by people creating new schools. For example the "University of Pheonix" is not a higher-prestige school than Dartmouth College.
You can substitute "college" for an unknown institution that might be either a college or universtiy, but not the other way around. For example, you'd typically say "After high school, I'm going to college" and not "...going to university".
Also, within the organization of a school there is a distinction in that a university can be made up of subsidiary schools that are called colleges. For example, the University of Illinois contains a College of Engineering, a College of Letters and Sciences, etc.
From my experience, a University is a collection of Colleges. I went to Lehigh University, which is composed of three (at the time) colleges: A business college, an engineering college, and the arts/sciences college. Each one is it's own degree granting institution. I think this is the majority of cases.
There are some exceptions to this, such as Dartmouth College which is technically a University since it is comprised of other sub-colleges (Tuck School of Business, Geisel Medical School, and Thayer Engineering). While they agree with my said definition, they opt to keep their "College" name for traditional reasons.
In the US, most standalone colleges (for lack of a better word, I mean those not a division within a university) do not offer graduate programs where students can obtain an advanced degree (Masters, Doctorate, Law). For advanced degrees, one goes to a university after receiving the undergraduate degree. Most universities offer both undergraduate degree programs and graduate degree programs.
In Britain one might say, "When I was at university...". That locution —at university— is not widely used in the US; it is regarded as a Britishism. Instead, we say "When I was an undergrad" or "...in school" or "...in college" or "... at Harvard" or "... at UCLA" .
In American usage, a "college" gives bachelor degrees, i.e. 4-year degrees. A "university" can give bachelor degrees but also masters degrees and doctorates, i.e. degrees that require more than 4 years.
I understand that British usage is different, that in Britain colleges are subdivisions of a university or something like that. Can someone knowledgeable about British usage chime in?
In the US (and many western countries) a university is an umbrella for several colleges. So within a university there would be a college of science, college of math, etc.
In the US you attend college (not university). The word university is used in the name of each school (i.e. New York University), but the word college is used when speaking in generic terms. For example,
"I would like to major in English in college",
"He is a college graduate"
are good examples where college should be used. As said before, the only time University is used is when referring to a school by its proper name
"I attended Harvard University for undergrad"
is a good example.
Also, if you get a Ph.D. or an associates degree(2 year degree), you are still a college graduate. If you have a Ph.D. you can use the title doctor. Otherwise, there is no way to determine what kind of degree you have, or the prestige of the granting institution without explicitly asking for the proper name.