A principle is an idea, often internal to a person or a culture. It is part of a moral or ethical code. Scientifically, a 'principle' is also a basic idea or concept. Rules (and laws) - either in the scientific or social sphere - are based on principles. Rules are decided on by people, written down and supposedly followed (or broken).

Basically, principles are unspoken and based on morality and culture. Rules, on the other hand, are written down and usually based on specific events. For example, stealing is against principle. We know it's wrong to take something that isn't ours. However, people steal all the time. To deter thieves and punish them, we created rules against stealing.