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It's pretty rare that the titles of Pokemon games have even a remote connection to the storyline.
>Red/Blue
Charizard and Blastoise, nothing to do with the story though
>Gold/Silver
Ho-Oh and Lugia, once again, nothing to do with the story
>Ruby/Sapphire
Groudon and Kyogre... Kind of. The colour of the gem is the only thing that matters, the actual reference of being a gemstone is meaningless though.
>Diamond/Pearl
Nothing at all. Literally zilch. Sure, Palkia has some crystals on his shoulders (which, to be honest, share nothing but their shape with real pearls) and Dialgia is steel-type (with diamonds being very hard) but that's about all. Diamonds and pearls have literally nothing to do with anything else in the game.
>Black/White
Reshiram and Zekrom, plus a few little stylistic things. That's it.
>X/Y
Just the rough shape that Xerneas and Yveltal have. I don't think there's any other references to "X and/or Y".
>Sun and Moon
I highly doubt it will have anything to do with the games beyond "hey these 2 legendaries are counterparts to each other, one is slightly orange and the other is slightly blue".