Am I correct in assuming voltage is used to describe two different concepts?
Both your concepts seem to be somewhat poorly worded

... being the force a voltage source applies to a conductor to get current flowing

Let's not deal with 'to get current flowing', dynamics is yet another problem, let's just handle the steady state. If you've set up a situation where current flows through a conductor, then there is a voltage across that conductor. Neither 'causes' the other, they both happen at the same time. Their ratio is referred to as the resistance of the conductor. Some materials will have a reasonably constant and linear resistance, metals for instance, and these get used for 'resistors'.

... and the other being the amount of energy required to get a charge from one point to another. for example, the energy required to move an electron through a resistor.

Voltage has the units of energy/charge. If one unit of charge, one Coulomb or one ampere.second, takes 1 Joule of energy to move it from one place to another, then there's one Volt potential difference between those places. For instance if a resistor dissipates 1 J of heat when 1 C flows through it, then there's 1 V across it.
The first definition is talking about moving charge through a resistor. It's expressed in hand-wavy terms, but it can be made exact with the concept of resistance. It's unfortunate that it seems to express a causative direction 'the voltage causing the current'. Either can appear to cause the other, depending on how you set the situation up.
The second definition is talking about moving charge from anywhere to anywhere, including through a resistor, and the energy required to do that, as a basis for defining the volt.