What is money?

I have come to believe that there are in essence two perspectives to understand money. Like the wave-particle duality two contradictory concepts seem to hold validity in describing what is actually going on.

a) Money is a claim earned by creating value to get something of equal value back.

b) Money is a public monopoly to allocate resources.

Looking at the world it strikes me as obvious that only a) can lead to a free and civilized society while b) must lead into tyranny over a long enough time frame.