Does potential difference only indicate how much energy each coulomb have, or make current flow, or do both?

 

Makes current flow.

 

It's a measure of how much energy will be transferred between the electric field and the electric charge as the charge moves between the two points involved. Since systems like to seek lower energy states, charges tend to want to move from higher potential to lower potential (keeping in mind that charges can be either positive or negative). But just because they want to doesn't mean they will or can. The flower pot sitting on the table wants to be on the floor and, given the opportunity, will find a way to get there. But if the table is nice, flat, and steady, the flowerpot will continue sitting there in a higher energy state looking stupid. The same with charge and voltage potential differences.

 

Does potential difference only indicate how much energy each coulomb have, or make current flow, or do both?

The former. High voltage is like a high mountain lake or a water tower. If there’s no outlet, there’s no current, but the potential is there.

If the resistance is finite, then so is the current, per ohms law.

 

It similar to water pressure in a pipe.