How does a theorem differ from an axiom in an axiomatic system?

In an axiomatic system, the distinction between an axiom and a theorem lies in their role and derivation within the logical structure:

• Axioms are the foundational starting points of a system. They are unproved formulas or first principles that are accepted as true—often because they are considered self-evident or particularly useful—without requiring a formal proof.123
• Theorems are formulas that are derived from the axioms. A theorem is established through a rigorous proof, which consists of a finite sequence of well-formed formulas where each step is either an axiom or a statement inferred from previous formulas using established rules of inference.143

Essentially, while axioms serve as the basic premises upon which the system is built, theorems represent the conclusions that can be logically deduced from those premises.52