It happens to me both in my car and motorcycle. I would expect to see the same value. For example if I connect it to the headlight fuse and I turn on the headlight or fan or using the signal light, I see a significant voltage drop in the measured voltage. Same when I connect it to the lighter socket, any consumer I turn on causes a drop in the measured voltage.
This is called "voltage drop", when electrical current flows through a conductor some power is always consumed by the resistance in that conductor (wires, or load, eg lights). Since there are no perfect conductors, there is always some voltage drop.
The more sensitive your voltmeter, the more visible the voltage drop will be when you measure it.
In addition to Cameron Roberts answer, there is also INTERNAL resistance in the battery. So an unloaded battery may show 13.6V (or whatever is normal) but that voltage will drop as the load on the battery increases.
Let's say, for the purposes of argument, that the internal resistance of the battery is 1.0 Ohm and it's nominal voltage is 13.6V. If you draw 0A from the battery you will measure 13.6 since Ohm's law says that V = I*R. Since I = 0A the voltage drop is also 0V and you read the battery's full output voltage.
If, however, you load the battery so that 1A is being drawn from it, now you will measure 13.6 - (1 * 1.0) = 13.6 - 1 = 12.6V. If you load is also at the end of a wire you will also have to factor in the voltage drop over the wire but you are starting with 12.6V now instead of 13.6.
When calculating the voltage available at the load you must factor in BOTH the wiring resistance and the battery's internal resistance.