What is the difference between definition and theorems? Geometry help

Is there a difference between the definition of isosceles triangle and the isosceles triangle theorem when using them in proofs? I put the isosceles triangle theorem on my proof, but the answer key says definition of isosceles triangle

An isosceles triangle has two congruent legs. That's the definition. So if you prove that two legs are congruent, then you can say the triangle is isosceles by definition. Conversely, if you know a triangle is isosceles, then by definition, it has two congruent legs.

The base angles of an isosceles triangle are congruent. This is a theorem, not a definition, because it can be proven. So:

(a) If you know a triangle is isosceles, then it has congruent base angles by the isosceles theorem, and

(b) If you know two angles of a triangle are congruent, then it is isosceles by the same theorem.

The difference is that the definition says what an isosceles triangle is, while the theorem is a proven consequence of the definition.