A premise is any statement that is used to support something that the author is trying to prove. It could be a fact, an opinion expressed as a normative statement (we should do x), a general principle or rule, or any other statement. Premises are just the statements and author uses to support a conclusion.
A principle is a general rule or statement. It can be normative, like all people should try to be kind, or descriptive, like kind people tend to earn more.