Axiom is recognized, but no one has come up with a way to prove it, and there is no way to prove it wrong, so it has become an axiom.

If one day an axiom is proved in some way, it will become a theorem.

I don't think your teacher has taught you why the distance of parallel lines is equal everywhere, so it is an axiom.

It can be proved that a point outside the connecting line has the shortest vertical line segment with the straight line, so it is a theorem (vertical line and other line segments, plus straight line, can form a triangle, and it is a right triangle. The hypotenuse of a right triangle is larger than the right.