WoW uses Shards to split the game world into several servers and then Instances to split off players from each Shard. Eve does the same thing with missions but only has one Shard.
The difference is if you meet a Eve player in real life your characters can meet in game, but in WoW it's unlikely for two random people to play on the same shard/server.
The game design makes that much easier to do. WoW has 4 continents with no loading screen (except for moving into instanced dungeons or battlegrounds) on each continent. By contrast, EVE is split into several thousand star systems. So while WoW has to put each continent on its own server, EVE can be as granular as to put each star system on its own server (though they usually use virtualization to run dozens of systems on one machine).
That's why WoW has to be sharded - each shard can only be split into 4 servers, whereas EVE naturally splits up by solar system.
It might look that way to a player, but if everyone on a continent moved to the same zone the game does crash. Also, you can't drag a mob vary far from its home area.
On the client side loading screens had more to do with loading textures for each zone to your graphics card than they did with handing off your character from one server to the next. You might not see a loading screen but if you gate home they still show you as the textures are loaded.
The difference is if you meet a Eve player in real life your characters can meet in game, but in WoW it's unlikely for two random people to play on the same shard/server.