【Principle】 , 【axiom】 ,  【fundamental】 ,  【law】 ,  【theorem】  are comparable when they denote a proposition or other formulation stating a fact or a generalization accepted as true and basic.

【Principle】 applies to a generalization that provides a basis for reasoning or a guide for conduct or procedure.

【Axiom】 can apply to a 【principle】 that is not open to dispute because self-evident and is usually one upon which a structure of reasoning is or may be erected. Perhaps more frequently the term implies a 【principle】 universally accepted or regarded as worthy of acceptance rather than one necessarily true.

【Fundamental】 usually applies to a 【principle】 , but sometimes a fact, so essential to a philosophy, religion, science, or art that its rejection would destroy the intellectual structure resting upon it.

【Law】 applies to a formulation stating an order or relation of phenomena which is regarded as always holding good.

【Theorem】 applies to a proposition that admits of rational proof and, usually, is logically necessary to succeeding logical steps in a structure of reasoning.