You would be incorrect if you think that.
The OP did not ask the difference between a university and a college, which is what you answered, but between a school and a college. An example that would apply to the OP’s question would be UPenn, which has 4 undergraduate schools/colleges. College of Arts & Sciences, the School of Engineering and Applied Science, the Wharton School, and the School of Nursing. In the case of Penn, my guess is their naming convention is that schools issue both undergraduate and graduate degrees (or graduate degrees alone) and CAS is purely undergrads. But I do not believe that is a rule set in stone, as Columbia does not follow the same naming convention (e.g. Columbia University Vagelos College of Physicians and Surgeons and Columbia Business School).
But getting back to Penn, my guess is a common question when first-years meet is “What school are you in?” While someone could be pedantic enough to point out the interlocutor’s error in both terminology and grammar, most people know what was meant.
Also, since the OP did not ask, I did not discuss the difference between colleges as being a constituent of a university vs stand-alone entities.