What is the difference?

If someone is selling something, and I take one and tell them that I will pay them later, then I owe them $$$.

Or if I borrow $$$ from someone, then I owe them that $$$.

Now while that person is owed some $$$, it does not mean that they deserve that $$$.

When does a person deserve something?

It seems that a person deserves something, when there is some kind of meritorious work in the discussion.

If I study hard for some exam, then I deserve a good grade.

It also seems that if you deserve something, then you also are owed that something. The reverse is not true.