When a pattern gives a gauge and the pattern also requires both knitting flat and in the round, does the designer assume:a) the same gauge for both, andb) if so, that the knitter can actually knit the same gauge for both?
I expect there are people who can get the same gauge knitting flat and in the round, I'm not one of them. If not otherwise specified I would do an in-the-round gauge if the part of the project that is most important to meet gauge is in the round or flat if the more crucial part is knit flat. Say for a sweater knit mostly in the round, I would do my swatching in the round. I don't know what assumptions the designer may or may not make. Others will know a lot more than I do.
I think what you wrote sounds reasonable. My gauge isn't all that different in the round vs flat, though sometimes I can see it. I knit english, that may make a difference too.