I've no idea what you're talking about. On-campus accommodation is "halls [of residence]" in the UK, "dorm[itorie]s" in the US, and "living on res[idence]" in Australia. A college is a non-university tertiary institute or TAFE, or a sixth-form separated from a school, or a division of a university.
Anyway, this is Studentenwohnheim in German.
Then it must only be Australia that uses it this way. In Australia, a college is a place at a university people live. For example, I was at college for my first year of uni, but moved into an apartment for the rest of the degree.
A college can also be "a division of a university" e.g. The College of Physical Sciences, The College of Mathematical Studies etc. You can make the argument that the colleges you stay in also fall under this category; but even so, asking an Australian if they're at a college will be understood to be a question about their living arangements (unless the question comes from an American, because we know what "college" means there).
In the US, we call them universities. We don't use that abbreviation. A college is generally within a university, or can be stand alone, such as a campus of a university. There are also independent colleges, which are generally smaller institutions that are limited to undergraduate programs. A two year program would be at a community or junior college, not a university.
"College" is used colloquially in the US for a college or University, but if you referred to a specific one, you'd use the proper name. But you can refer to a student of either as a college student, and a college student would typically say "I go to college."
It would be a mistake in the US to assume that you can always say college instead of University.
Basically it means the same. I would say the difference is how often it is used. Uni is more common. You could say for example "Ich habe morgen Uni." (I have classes at the university tomorrow), you wouldn't use Hochschule here. Another difference that is possible is that you would call a former Fachhochschule Hochschule and not Uni. Fachhochschulen (that today are called Hochschulen, though Hochschule is a synonym for Universität as well) are very similar to universities but slightly more practically orientated.
In the US, I've never heard "Uni" used to refer to "university". Instead we generally may say "college" or the use the complete word "university". More accurately, colleges are smaller. In fact, a university in the US may have several "colleges" within it, for example the college of engineering or the college of arts & sciences. Each college offers a degree program in their respective field, but are both part of the same university.