To be prudish is to be extremely proper, almost a little too proper. To be called prudish isn't a compliment.
To be proper is to be polite and have good manners. To be prudish is to take being proper to an exaggerated or ridiculous degree. For example, it's definitely a bad idea to use a naughty word in class, but a friend who scolds you when you use it privately could be considered prudish. They're going a little too far. Prudish behavior is also called priggish, prim, prissy, puritanical, and straight-laced. Others usually think prudish people should lighten up.