Is there any difference between a math invention and a math discovery? [closed]

From wikipekia:

The calculus controversy was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented in part by their disciples and associates – see Development of the quarrel below) over who had first invented calculus. It is a question that had been the cause of a major intellectual controversy over who first discovered calculus, one that began simmering in 1699 and broke out in full force in 1711.

I'm just curious if in the field of mathematics it means one thing to invent and another to discover or if they go totally hand in hand.

Connes, the Fields medalist, and Changeux, a celebrated neurophysiologist, have had an interesting discussion on that subject.
It is this book.
And here is paper commenting on the book.

I just want to point to the fact that this is indicative of a somewhat bigger question. Is mathematics simply descriptive of reality or does it exist on its own in a Platonic existence? For instance, was Fermat's Last Theorem true before it was proved by Wiles? Mario Livio wrote an interesting book exploring this question. It is called Is God a Mathematician. He concludes that certain concepts may be invented, such as calculus, but then the results are discovered as inexorable deductions from the invention.