This new mode they are teasing is obviously related to some story/Subspace Emissary 2 type deal
I'm not sure of this myself. If there's an actual story to the game I would expect Sakurai to try and hype it up from the very beginning like he did in Brawl.
So far we've been shown boss characters and stages that look like would work in an Adventure Mode kind of thing, but they've been presented so nonchalantly I doubt it will be that big of a deal (the new mode was basically "hey there's this new thing, but we'll talk about it later").
As for the Heroes vs. Villains thing I think has to do more with the fact every character has its own Story Mode set of stages so it's fitting.