Both postulates and theorems are derived from deductive reasoning. A postulate in philosophy amounts to spoken or written common sense, in that it is regarded as the answer anyone who took the time to investigate the question would come to. Theorems, on the other hand, require a postulate to arrive at a proposition. The logic of a theorem may be simple to follow, but it must be explained, usually in the form of a formula or rule, such as an "if-then" statement.
Philosophy bases much of its logic on fundamental principles, whether to unravel those principles or to develop new ideas based upon them. A postulate is a fundamental principle. It forms the framework for philosophical logic that forms the basis of a theorem. The theorem may be a principle, but only in so far as it is a formula or law. For example, one mathematical postulate is that between any two points there is a line. A theorem based on this postulate deduces if A, B, and C are distant points and AC + CB = AB, then point C lies on the line connecting points A and B.
A postulate does not have a burden of proof. The proof of a postulate is considered self-evident, or assumed, without a need for additional reason. A postulate is an axiom, taken for granted and accepted as true. A theorem is a proposition that is deduced from postulates or other formulas. It either remains to be proved or has been proved.
Theorems require a system or framework in which to operate. The self-evident nature of a postulate means that it can exist alone without any network of ideas for support. Postulates stand alone in their function, and nothing more is required of them.