In the US there’s really no set differentiation. There’s no rules that colleges have to be private or universities have to be public. Harvard is a college (undergrad) and a university, neither are funded by the state.

The general way it works is, universities are large, colleges are small… however, there’s even exceptions to that, if I remember right there’s a university in Alaska that only enrolls like 300 people. A lot of colleges in my state are state funded because they are 2 year community colleges. A lot of our universities have 4 year liberal arts colleges at them.