W introduced the Foundation X, which while it didn't completely live up to it's potential (like Quantum in the recent Bonds), it was involved with Fourze's plot in the background, and the crossover movie. Decade showed up in the last few episodes of Wizard, as did Gaim before his own show just started, so regardless of whether or not you like the first 2, showing the Rider who caused the fusing of all worlds and the then most recent rider plus his successor in the episodes rather than in the disputed crossover movies suggests they are all in continuity now.

How exactly? Besides perhaps a heavier focus on gimmicks I don't feel they've gone in a particularly different direction at all.

Fourze Episode 2 did show footage of Rider 1, Super-1, Kuuga, and had a report on the destruction of Fuuto Tower in Double's movie. So...

No one should ever use a fan-made term because it's...fan made? Fans make up names for all kinds of things, I don't really see how that's a problem. Obviously the Heisei era didn't end with Decade, but it did change in some ways. Having a shorthand term to refer to that doesn't really strike me as being a bad thing. Hasn't Toei used the term "Heisei Phase 2" for that, too?

Well I feel like that there is more of a continuity with the shows now then it was before Decade. The final episodes of each show since W expect for Gaim contains a link to the next series and a few of the Winter crossover movies have fit into the timeline of the shows pretty well. Like you said that there is more a gimmick focus in the shows too. I also feel like the tone in the recent Rider shows do feel a bit more then Kuuga-Decade did, but that's just me.

What's the difference between Ryuki's, Knight's and Zolda's colored spandex & the black spandex riders?

The colored ones are the main characters. I guess?

I've heard that the characters with the colored undersuits are the main characters/long-term characters, which were planned from the start. Ouja was supposed to be a minor character (hence the black suit) but his popularity lead to him being one of the "main four" despite not having a uniquely colored suit. I don't have a source for this, I've just seen it around.

Yeah, this is what I've heard, too.

It's still Heisei though. Just call it Heisei. We don't subdivide the Showa era based on number of shows or anything. There's no real reason so subdivide the Heisei era either. This particular fan term makes no sense given the context of the franchise though, so that's why I don't care for it. Use it if you want, that doesn't make it correct.

The only thing that changed with the post-Decade riders is a possibly that it's a more gimmick & collectible trinket driven franchise now. And we get more previous hero team-ups than we ever did before. But ultimately it's exactly the same. Toei doesn't distinguish the two, so why do fans feel the need to do so?