University you get a degree from. You have to pay for the course (a big yearly fee). Most undergraduate courses are 3 years, medical courses like dentist, doctors are 6 years. Upon completing that you can go on to do a Masters degree in a specific subject which is an extra year (this is what I did), and after that, you can go on to do a PHD which is another 3 years where you have to write a huge massive thesis on a certain topic.
In University you have lectures (usually just a few hours a day) and you go out drinking a lot, and do all sorts of crazy stuff in your spare time. You'd usually live on the University campus for your first year (and sometimes second) before moving into a house with your friends.
College is an extension of school. Most people go to college after leaving school at the age of 16 (you'd wait to finish school at 18 to go to University), and you'd go on to study various courses that range from learning a trade, like carpentry, plumbing, bricklaying, electrician etc, or a beauty course (for girls (and some boys I guess)) IT and computers etc.
Some people also go to college to do their final 2 years of school instead of staying in school to complete those exams.
The qualification you'd gain from college varies from course to course. The qualification I'm getting for example is a Level 2 diploma and NVQ in Electrical Engineering. I'm also getting some other qualification which I can't remember what it is lol.
Also, you'd be staying at home if you were at college, as they don't provide halls for you to live in.
But in short, yeah, there's a massive difference between both. Take it from a guy who's experienced both!