Belief and Principle

Belief

A belief is something that one accepts as true or real. Often belief refers to a religious conviction. In a more general sense, belief means trust, faith, or confidence in something.
Ex: Despite the differences among Christianity, Judaism, and Islam, these religions have a number of beliefs in common, such as the belief that there is only one God.
Ex: John's belief in the value of hard work is unwavering. He is convinced that you can obtain anything you want as long as you're willing to put in the effort.
The expression contrary to popular belief is used to introduce a statement that is contrary to what most people believe. You can also use the expression beyond belief to emphasize that something happened or is true to a great degree.
Ex: Contrary to popular belief, drinking bottled water may be worse than drinking tap water. Not all bottled waters are purified, so some are the same quality as tap water.
Ex: We were shocked beyond belief when we heard that Mr. Resnick was accused of embezzling the school system's funds.

Principle

A principle is a moral rule or belief that guides one's actions and helps one know what is right or wrong. Principle can also refer to a fundamental truth that serves as a foundation for a system of beliefs. In scientific contexts, a principle is a natural law or fact that explains why something happens or how something works.
Ex: One of the fundamental principles of human rights is that everyone by birth has certain rights that cannot be taken away from them regardless of what they do.
Ex: Causality is one of the most basic principles of physics. In simple terms, it means that every effect must have some cause.
In principle is a synonym for fundamentally or in essence, and it is usually said about something that is done without consideration of specific details or special situations. On principle means according to one's personal rules for correct behavior or also according to a fixed rule or practice, like a habit.
Ex: Both parties agreed to the bill to reduce the tax burden in principle, but they disagreed on precisely what measures should be taken to reach that goal.
Ex: When Martin takes a girl out on a first date, he always picks up the bill on principle. He thinks it's a nice gesture.