Postulate

A postulate, also known as an axiom, is a statement or proposition that is accepted as being self-evidently true without the need for proof. In mathematics and logic, postulates serve as the foundational assumptions upon which a system is built.

While postulates are assumed to be true and require no proof, theorems, on the other hand, are statements that need to be proven, typically using the postulates of the system as a starting point.

Theorem

A theorem is a statement that has been proven to be true within the framework of a mathematical system, based on the system's axioms and previously established theorems.