The Pokemon series (of games, not Pokemon the Series) has always had this quirk of releasing in pairs of nearly identical games with a few of the Pokemon scattered across the two. Supposedly, this is to encourage trading, since you can't get every last Pokemon with only one game, and would have to trade with someone else who has the other. But I'm not entirely sure if that's what Game Freak intends by this anymore, or how effective it was in the first place, so I'm going to collect my thoughts and theories on the matter in this page.
I should note, I haven't done much actual research on this, so this is all based primarily on incidentally absorbed information. If you have any corrections to make, by all means, make them.
Even though I wasn't around when the first Pokemon games were being played, I imagine the idea behind the split versions was this:
You, an E10+ year-old, are playing Pokemon Red, because it has a huge dragon on the cover. Maybe you're already trying to fill up the Pokedex, or maybe you're just having trouble getting past a gym battle. Either way, you find another kid playing Pokemon on the school playgrotund, or the town playground, or the backyard playground of a relative's house, or whereever kids who play Pokemon used to gather those days, and the two of you start looking through each other's PCs to see if there's anything you want to trade.
Most of the Pokemon he has, you already have, too; you've both thoroughly paced around in every patch of tall grass you could find, and caught all the Pokemon you can. Then, you notice a name on his screen you don't recognize. When you check its summary, it has a sprite you've never seen and a cry that takes a trained ear to differentiate from all the others. He has a Pokemon you could never find, and, as it turns out, you have one he could never find either.
You happily make the trade, knowing where you can find more of the Pokemon you're trading away. You then go on to crush that gym, or that Pokedex, or whatever it is you needed that weird little guy for. Plus, you met another kid with at least some similar interests that day.
Now I actually think that's a neat little idea, having completing the Pokedex not just be a bunch of solitary video gaming, but looking for people who have Pokemon you don't and giving them Pokemon that they'll get more use out of than you were. That's a great way to bring kids together and the idea of making a system that encourages and incentivises sharing is noble for a kid's game.
However, there are a couple arguments you could make to say that this is ineffective, unnecessary, or just flat-out not the real intention in newer games.