The Mystery Dungeon games are similar, but not identical, to the main series games.
Red and Blue Rescue Team is the same game, with only very minor differences. The only real difference is some version exclusive Pokemon and Items. So its like the core games. The story is very simple, and basically everything is the same across all the games. I can't really talk about the 3DS games since I haven't played them,
The Explorers games, are very different story wise. Bar a few returning characthers (basically just the shopkeepers) the games feature an entierly new plot, brand new characthers and a whole new world to explore. The mechanincs remain the same, the same dungeon crawling, the same battle system and the same mission system. Some mechanics were reworked, removed or added (no more Friend Zones, remodled recruiting and bount missions for example).Explorers of the Sky goes further with this, adding even more content (but maintaining the story of the first Explorers games). Here we also see some proper side quests, not featuring the main charcthers, but rather an assortment of sidequests and side-characthers. Bar that, the Explorers game have the same story. Also added in the Explorers games was the Gen 4 Pokemon. The graphics remain fairly constant, and so does the battling though.
The first Explorers games did do one thing exceptionally well, being sequels. They took the mechanics of Red and Blue rescue team and expanded upon them. The games are far more streamlined and smooth in terms of gameplay. The characther's are funny, and you genuinly care about them and they are all memorable. The games are just a blast to play.
But the most important upgrade went into the story. The Explorers games feature the (in my opinion) best story out of all Pokemon games. It feels big and important right of the bat. It have great foreshadowing, building up to a heartwrenching climax. Where the first game's ending feelt a little rushed, this one let you carry the weight of the world on your shoulders.
And unlike the first game the story dosn't end. The postgame content is massive, bigger than the first part of the game even. There's so much to do you'll be playing for weeks.
It throws so many great moments and curveballs at you I'd be ashamed to spoil any of it here, so just take my word for it. The sum of all this is thus:
The story of the Explorers games isn't the same as in Red andBlue Rescue Team and the story is far, far better than Red/Blue Rescue team.
Note: If you are thinking about playing the Explorers games, Explorers of the Sky is the preffered version, due to the added content.