Think of it this way. Rules typically come from outside yourself. Principles come from inside yourself. At the end of the day, you have to live with yourself.
A rule is written to control something, for example stopping at a red light. The rule exists to control the flow of traffic and prevent accidents. A principle related to this rule is that "I believe that most rules (not all) are there to protect me." Therefore, your principle will apply to the rule for red lights, and several other rules as well.
When a rule violates a principle, this is when you have to decide: is my principle actually a real principle, or just a preference. How to know the difference? If you are willing to lose friends, or go to jail or die for it, it's a principle. Otherwise, it's just a preference.