Addressing just the reason why voltage varies, you are correct in thinking line losses play a role. No normal wire is a perfect conductor. Superconductors come very close, but for those of us working with normal electrical components, wires are just small valued resistors. As such, they experience a voltage drop when current flows through them, by Ohm's law. This is also why long-distance power transmission is done at high voltage, and stepped down as near to the customer as pratical.
You can observe this directly when a motor in your fridge, air conditioner, or clothes dryer turns on: the high starting current of the motor pulls the voltage in your house down, dimming any incandescent lights. Of course the running current is much less, so the lights appear to return to their original brightness, but if you were to measure carefully you would find they are a tad dimmer than they are without the motor running. With a large AC compressor even the current after starting is significant enough to dim the lights until it switches off.
Of course the electric utility attempts to mitigate this effect, but nothing is perfect.