A relation can be a set of ordered pairs, like you stated.

i.e. {1,1} {3, 5} {4, 14} etc.

A function is a formula from which you can derive ordered pairs.

If the function is you can derive infinitely many relations by plugging in numbers. Let's get a relation for 0 < x < 3

{0, 0} {1, 1} {2, 4} {3, 9}