There was a thread like this a few months ago but it's outdated due to BW. I suppose we can talk about it again. It's not all that much of a talked about topic.
The third games are:
The remakes replace Blue and Crystal in the timeline, but you can put them into their own alternate timeline.
A lot of people in the west mix up what the third Gen 1 game is, saying that none of that happened or referring to the differences from the other two games. But Yellow is the fourth game, not the third.
From what I've heard in BW..
The third games are a middle ground between the first two games in terms of Pokemon, add new events, and add more depth.
A lot of people think HGSS proofs Emerald isn't the canon game due to Steven saying he's the champion. It appears champions cling onto their titles though or people aren't looking at the context. Didn't he retire as a champion anyway?