Two different meanings of "distribution." Think "probability distribution," not "transfer."
A metaphor is when you literally talk about one thing, but are actually referring to something else. I'm not doing that here. When I talk about time, I'm actually talking about time. I'm comparing it to money, not using it as a metaphor for money.
As for what they have to do with each other, it's simple:
The usual way to allocate scarce goods is to use supply and demand to set an equilibrium price, and then let people spend money in order to obtain it. Another way to allocate scarce goods is to require people to spend time in order to obtain it.
People tend to consider the first way to be unfair, especially for goods with high emotional value, and whose cost to produce is not connected to the price. People tend to consider the second way to be more fair, because time is more equally distributed among humans.
The first paragraph is fact. The second paragraph is observation and speculation. No metaphors in sight.