My parents and grandparents were always particular that there is only ‘Gut Shabbos’ on Shabbos (and woe betide you if you didn’t say Good Shabbos to them.). No good morning, goodbye, good night or anything else. I never realised there was any other way until I met my wife’s family.
We also don’t have the minhag not to say Good Shabbos after mincha. But apparently it’s got to do with Dovid HaMelech being niftar then.