Just like D&D ripped off Tolkien but added its own touches to make the concepts better suit what it wanted (a tabletop RPG), and just as Tolkien ripped off classic myths but modified them for his purposes, Warhammer and Warcraft both modified their ripoffs for their own purposes.
And their own purposes are very similar.
Neither of these settings started out as an MMORPG. Warhammer was originally a miniatures wargame. Warcraft was original a real-time strategy game.
All of the gameplay in a miniatures wargame is "I bring my army of miniatures out to fight your army of miniatures". An RTS isn't necessarily geared at playing against human opponents; Warcrafts 1 through 3 had fairly extensive single player campaign modes. But the people who love the game and play it the most are the ones who play against other humans.
Why is this important?
Because with both Warhammer and Warcraft, any two opponents might be playing any two armies. If you play Warhammer, you might decide to buy an elf army and your three friends might decide to get dwarfs and Chaos and, hey, another elf army. In Warcraft, your favorite army might be Undead and your buddy's favorite could be orc. Or anything.
When you sit down to play either one, you're going to play your favorite and so it your friend.
Either game could have said "one opponent needs to play side X and the other side Y", just like Axis & Allies doesn't pit the USA against England. But this would have arbitrarily limited the options. If neither of us likes playing England, why make one of us play England? Couldn't we pit Germany vs Germany, somehow?
That is what the Warcraft and Warhammer settings are intended to represent. The armies may have loose default alliances, but the background describes peoples so fractious and divisive that one can easily imagine allied armies turning on each other -- or even people of the same race fighting one another. It doesn't break the flavor of the setting to have Tauren fight against Tauren or Elf against Elf. That kind of thing happens in this setting.
Thus, the two "sides" in Warhammer, Order and Destruction, and the two sides in Warcraft, Alliance and Horde, are not Good vs Evil. Because Good doesn't fight Good. Good doesn't even fight Evil if it can get a chance to establish peace and prosperity and convert Evil instead. The games do not want the sides to establish a peaceful and prosperous society, because they've got no game mechanic for making peace or prosperity entertaining. These are games about simulated fighting aimed at players who enjoy simulated fighting.
Some games make their setting at odds with their gameplay and expect players to overlook the inconsistencies. These games made the opposite choice: "players are supposed to be fighting anyway, why not give them a reason to do so?"
Warhammer's setting features the epic struggle of Evil against Not-Quite-So-Evil. Order is not Good. It's not even good. The High Elves are snobbish bigots, the Empire operates under religious totalitarianism and the executions of heretics (or anyone who looks heretical), and the dwarfs fight to the death over centuries-old grudges about such matters as "your ancestor returned my great*10 grandfather's hedgeclippers bent".
Destruction is gleefully evil. Well, the dark elves, like the high elves, don't have much sense of humor, but the greenskins revel in combat and Chaos is staffed by traitors to humanity who hope that their twisted gods not annihilate them along with the rest of the world if they are victorious.
As a roleplaying or story setting, I dislike Warhammer. It's a miserable, unhappy place stuffed with unsympathetic characters.
However, as a setting for a game about killing each other, it works well. The Greenskins have the right idea about their universe: fighting is a game, and you whether you win or not it's a blast just to play. Ultimately, my character is going out to solve problems by blowing them up. Pretending that this is good and noble on my character's part has always been a stretch, and it's nice to abandon that conceit. Overall, I think Warhammer's dark universe was a good call on their part, because it makes the setting fit the gameplay they were going to have anyway.
It does, however, sort of make me want to play an MMO where the gameplay is all about establishing peace and prosperity and making stuff.