Who assigned numbers to the declensions and conjugations, and why?

1. How many noun declensions were there in ancient Greek?
2. What's the difference between a declension and a case?

How many noun declensions were there in ancient Greek?

In Greek there are three noun declensions: first, second, and third.

What's the difference between a declension and a case?

In Latin, not only is word order used to indicate what role a noun plays in a sentence or clause, but also what is called a declension and case. A case tells the speaker or reader what the noun does or is doing, and the declension of the noun decides how the case will look.