You can't argue that GBC didn't "correspond to" N64. N64, which was of the same generation as PS1. So GBC was of the same generation to, and therefore "corresponded to" PS1 in that fashion. GBA clearly "corresponded to" GCN; they had a range of hardware and software connections, and even launched the same year. GBA corresponds to the 6th generation of consoles in this way. DS and PSP may have launched a couple of years before their home console big brothers, but they were undeniably of the same generation. Now 3DS and Wii U are going to have cross-play functionality. They belong to the same generation. The eighth generation.
Vita's cross-play with PS3 is a weird case stemming from the PS3's long lifespan. Undoubtedly when PS4 launches, it will feature more Vita cross-play functions than PS3 currently does... assuming Vita is still around to see the PS4 launch.
Nintendo's handheld consoles have always had a close relationship to their corresponding home consoles. They are the same generation -- especially when we start talking about software, which is what the context of my statement was. Just look at the Bit.Trip series. Not a very impressive technical feat at all, but it would be beyond silly to suggest that those are 4th-generation games or something. They weren't made in 1992. The fact that New Super 2 doesn't do anything that wasn't technically possible on GameCube doesn't make it a 6th-gen game. It was developed in 2011/2012, by developers who had experiences no developers in 2003 had. It likely incorporates programming techniques not yet imagined a decade ago. There's no argument to be had here; the tech isn't what determines a game OR a console's generation.
I HATE THEM
A console's "generation" is just a number to be thrown around. Whether Wii U is 8th-gen, 7th-gen, 12th-gen or 1st-gen, its "classification" is completely irrelevant and doesn't change a thing about its capabilities, its release date, its competitors, its third-party support, its launch price, or its color scheme.
That is all by design, being made by the same manufacturer. The same would likely not hold true had the handhelds been made by anyone else than Nintendo or Sony. Case in point, the N-Gage, released in 2003, bang on between the PS2 and the PS3.
Semantics, I love them, because they make us smarter and put people on the same footing. So much arguing is over the ambiguity of words. Words aren't concepts, they're tools to describe concepts. The sharper the tools, the cleaner the cut.
Again, generations have no reason of existence if not due to hardware upgrades that can't be done on the same machine.