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>RBYGSC Take place in the Gold and Silver Ages of Pokemon. Fun, lighthearted, nostalgic, with whacky storylines about time travel and such. Only a hint of seriousness. Think Gold/Silver Age Batman going into space and fighting dinosaurs as a parallel.
>RSEFRLG Take place in the Bronze Age of Pokemon. Things are shaped up and a little more serious while still adhering to slightly whacky storylines (The Earth either flooding or drying up, a machine that needs rubies and sapphires to work). Games like Colloseum show the more serious nature the Bronze Age is conveying. Again compare to Bronze Age Batman as a parallel.
>DPPHGSSBWB2W2 Take place in the Modern Age. Stories with way more serious undertones (Cyrus acting like Hitler, the entire Zuniga storyline). The events of FRLGRSE all count, much like Modern Age Batman counted stories like Knightfall and the Robin Origins. The most streamlined, consistent timeline, we can actually call this universe the Pokemon Prime Universe.
>XYORAS is the New 52. Pokemon brought into the modern day, with dozens of advanced mechanics and more science based stories. Like Batman in the New 52, the stories of the other games are implied to take place with slightly different spins on them much like how Jason Todd became the Red Hood in the New 52 (it's implied to have happened similarly but was never shown). All the past events are scrunched up and will be shown through remakes or specials like Pokemon Origins.