What is the difference between a US Commonwealth and a State?

My dad lived in Kentucky, which is a commonwealth state. He has a bad history with that state, and constantly bashes it and other commonwealth state. He says the laws are more "totalitarian" as i would put it, one particular law is that one can be arrested without having identification. I can understand that maybe he just had bad luck with the law. However i know that the Commonwealth status is just a remnant from older times, but does it affect their legal systems? in terms of laws and courts how do they, if they do, differ from "states"?