A student often meets quantum mechanics as a long list: superposition, Born rule, Schrodinger equation, uncertainty, Bell, no-cloning, Pauli exclusion, commutators, and so on. The list becomes usable when you sort it by job. A principle says what the world is allowed to be like. A law or equation gives the machine for predicting what happens next. A theorem uses those rules to prove that some classical idea cannot survive unchanged.

Think of building a lab protocol. Principles are the rules of the game, equations are the instruments you use to compute predictions, and theorems are the safety signs that say which classical shortcuts are impossible. You need all three to understand why a Bell circuit, a teleportation circuit, and a cryogenic qubit stack are part of the same theory.

The boundaries are not perfectly sharp. The Born rule is often presented as a postulate, while Gleason's theorem shows that its probability form is strongly constrained by Hilbert-space structure under appropriate assumptions. Pauli exclusion is introduced as a principle in elementary quantum mechanics, but it is tied to the spin-statistics theorem in relativistic quantum field theory. CPT and full spin-statistics are not elementary nonrelativistic quantum mechanics; they belong most naturally to quantum field theory. This module keeps those status labels visible so the result is not memorized out of context.