In my opinion, I agree with Nah that the majority PKMN fandom has taken a different meaning to the mentioned words when it comes to the PKMN games. I believe it's a silent yet accepted agreement since Blue(in Japan) and Yellow were made.
Third versions are "remakes" of the original pair, but with improvements, however it's mostly called as just that, "third versions".
The word "remakes" were properly used by the fandom when FireRed and LeafGreen were made, and again, the majority of the fandom has accepted to call these "remasters" as "remakes".
Sequels are only applicable to Black and White's "third version" games, which were B2W2. They are still considered as 'third versions' by the vast majority of the fandom, and also respecting it as a sequel.
You could say that Gold, Silver and Crystal are the sequels to Red, Green, Blue and Yellow, yet the fandom calls the Gen2 games as "a new generation of core games" or whatever.
You can even say that Sun and Moon are sequels to Red, Green, Blue and Yellow, because an aged Red and Blue are there.
Going back to the main topic of the thread, in my opinion, I agree with the majority of the fandom that Ultra Sun and Ultra Moon are 'third versions'.