Looks like the 3D Mario footage also shows Mario doing the triple jump again, which was removed in 3D World. There's also a heart icon on the right side of the screen in that Bullet Bill platforming section, which probably means a health system closer to the the previous 3D Mario's before 3D Land/World as well. So yeah I think it's safe to say, even with a few second of footage, the next 3D Mario is going to be closer to the either 64/Sunshine or Galaxy, then it is to 3D Land/World in terms of design.
And for Mario Kart, with King Boo playable as well as the ability to hold what looks like 2 items at once this is going to be a brand new title, probably even called Mario Kart 9. I imagine though they're just blatantly reusing the exact same engine and will probably still include a shitload of stages from MK8, but don't be surprised if we still get at least 16 new stages, because this is going to be considered a new installment. By the time the Switch comes out, it'll have been 3 years since the base game of Mario Kart 8 was released and 2 years since the last DLC was release. That's plenty of time for the Mario Kart team to make a new installment during that time and for marketing reasons alone is something Nintendo would want since new games make bigger impacts on sales then ports.