Definition of Source Power for RF Transmisison Line Source
While the physics of computing power remains the same for all situations, the context may require that you choose particular values for impedance or voltage, for particular power definitions.

In the context of RF, the 'source power' of a generator will usually be defined as the power it actually delivers into its defined system impedance, which is usually 50 or 75 ohms. This remains the definition whether the generator has an output impedance of nominally the system impedance, or very different from it. If it's different, then this is not the maximum power that can be got from the generator.

If you load a generator with a load other than the system impedance, then it will produce a different power. This new power can be computed in terms of the defined source power, and corrections to it based on source and load matching to the system impedance. This is one of the benefits of referring all measurements to the system impedance, it allows the details of source and load match to be handled systematically, and allows small corrections to be ignored.

When comparing different formulae for power, take care to understand where the voltage is being measured, so whether at the physical port from the generator, or at the theoretical voltage source that drives the theoretical output impedance before the port.