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>Classic: Gen I-IV
>Transitional: Gen V
>Modern: Gen VI+
I feel like this is the easiest way to explain it. You can do sub-groups within the groups (ex: Gen I and II being Pokemania, 3DS games vs. Switch games, etc.) and I think there's an argument to be made that Gen IX+ might be a new era if open-world becomes a mainstay,but I think most would agree that there's undeniably a pretty cut and dry difference between Gen IV and Gen VI.
I think it's hard to argue Gen V as belonging to either camp because it does things a lot of classic games don't (increased handholding and linearization, outside of Japan) while also doing things a lot of modern games don't (battles are still 2D, not 1-to-1 rehashing old Pokemon with Megas/exclusive Z-Moves/Gigantamaxes/regionals).
The only other way I think you could classify it would be
>Pre-Split: Gen I-III
>Post-Split: Gen IV+
but considering most of these threads exist for the sake of genwarring I don't know if anyone would be happy with that answer.
