No it doesn't. Different customers who buy at the same moment tend to get the same price (f they're shopping for the same fare type, such as deepest discount coach). The same customer shopping on a completely date tends to get very different price, even thought that's the same customer.

So (for a given fare type) the variation is not from customer to customer, it's from when one person buys to when a different person buys. (That is for a particular route. Obviously, on a plane, a person flying a connection versus a person flying just that route nonstop will also have a very different fare, but that's because they're flying completely different routes, even if they overlap with one leg on the same plane.)

And since it's based on time of purchase, not person doing the purchase, it is possible compare price in cash and award price at any given moment.

With a revenue-related redemption like Southwest's, that relationship tracks from to moment. With a region-based and tier-based redemption like miles-based airlines, even at a given moment the relationship is complex and hard to pin down (since at any given moment, it varies from route to route).