The same thing does happen with light, in that your simple first example does need to consider relativity if you want to be exceptionally precise. It’s not correct to suggest these two scenarios are fundamentally different, where only one needs lorenz corrections. In truth, both scenarios do, its just that the correction is so insignificantly small for the first example that it can be left out without any significant change in the answer.
The same thing does happen with light, in that your simple first example does need to consider relativity if you want to be exceptionally precise. It’s not correct to suggest these two scenarios are fundamentally different, where only one needs lorenz corrections. In truth, both scenarios do, its just that the correction is so insignificantly small for the first example that it can be left out without any significant change in the answer.