Why does the potential along a uniform current-carrying wire vary with the distance along it? Is it because as the electrons move further through the wire they lose more energy due to resistance?
Also, in this context, I believe potential refers to the electric potential energy but I am unsure, could someone please help,
Thanks.
 A: Yes, the potential and the potential energy is similar.
And yes, the energy loss is because of the collisions between the electrons and the ions. Especially if there are devices with resistance, a whole lot of energy does dissipate as heat to power those devices. 
This results in a difference in potential across those points of the device, and this means that there is a difference in potential energy.
A: There is a potential gradient because you connected the wire to a power source. 
A: Potential is the electrical pressure at a single point w. r. t. ground, like a static charge on an object. Voltage is the potential difference (pressure difference) between 2 points. Both are expressed in volts.
If you connected one side of a 12V battery to the active wire of the mains, the potential of the other terminal would be mains voltage ac + - 12Vdc, but a volt meter would measure 12V potential difference across the battery.
As for the wire: all wires have a bit of resistance, so when you pass current through it, there is a small pressure (voltage) drop along its length, like moving water in a pipe. 
