The Persians discovered the theory long before Pythagoras, but Pythagoras made it well known and proved it many times. He got the idea from the Egyptian rope-stretchers, of which you can ask another question for them.
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You can use pythagorean theorem twice to find the diagonal of a cube
pythagorean theorem was named from a greek mathemition called pythagorus (I think that's how you spell it)
The difference in the distance formula and the pythagorean theorem is that the distance formula finds the distance between two points while the pythagorean theorem usually finds the hypotenuse of a right triangle.
Pythagoras
Pythagorean theorem