Policeman = cop; Police = the cops. It is a disrespectful term and I would not use it. Origin stories are as above, constable on patrol. Also story of the copper badges being origin. Another story is the old verb "to cop" = to seize (or arrest), so coppers seized or arrested people.

Police is plural, cop is singular, but they mean the same thing-- except that cop is less polite. I think it originated in the United Kingdom from Constable On Patrol = COP = cop. In the USA it was altered to copper. You will hear that in old movies, but it is not used today. Cop is what you can call a policeman, but probably it is better not to say that to them directly. It is not polite enough to address them directly with it.