Let the Old-timer handle this one...
I remember playing the NES and SNES Mario games a long time ago, back before they needed re-releases on a bunch of consoles. The four core Mario games all had a different feel to them, but aside from the rehashed Doki Doki Panic of Mario 2, they were all pretty much the same.
They did have the Mario Kart spinoff for SNES, but everyone knew the formula for a Mario game until 1996.
Suddenly, you had a "new kind of Mario" to use the term we're using in this thread. Actually, you had two: you had Mario RPG and Mario 64. Both introduced a radically new gameplay engine (different for each) and even different feels for the games. Suddenly, Mario was much less arcade-ish and more of a story-based adventure. In fact, storylines started to really develop, particularly in Mario RPG.
The next step seems to be Paper Mario, which I never played in its entirety. We've had something in the ballpark of ten of these games and while they all seem to be a little different, they all have the same style of character and are all kiddy-type versions of Mario RPG (my opinion at least).
Mario Sunshine basically built upon Mario 64 but used the second stick effectively. Galaxy was really just the next evolution.
Everything else was something that had been done before. New Super Mario Bros wound up being, well, an updated version of the original games. They added 3D to it, but to me, Mario 3D World is really just a hybrid of what's been done before. Great game, but not one I'd call a complete innovator.
I'd expect this announcement to signal one of the following:
--A storyline that hasn't been done before (it's been nice to see something other than Peach get captured in some titles)
--Some new perspective or control system unlike anything that's been done before
--Redesigns of the characters (not complete redesigns, mind you, but enough to make them interesting again, sort of like Mickey was redesigned for Fantasia)
It could be all three, maybe a combination of things. It may not even be any of those. Still, if you look at history, the only "new kind of Mario" truly happened in 1996--on two occasions--and in 1999 with the Paper version.