Basically, its the courses from Mario Kart Wii without the retro courses, the battle courses, or those courses which appear in Mario Kart 7. Thats a total of 12 courses hence why I call it "Mario Kart 6" and not "Mario Kart Wii on 3DS". Those 12 courses would be redesigned slightly as the Wii courses appearing in Mario Kart 7 have been done.
The rest of the game would be identical to Mario Kart 7. Same characters. Same presentation. Everything. Coins and unlocked parts/characters earned on your Mario Kart 7 save file would carry over to Mario Kart 6. And when you gain coins in Mario Kart 6, they are also sent across to your Mario Kart 7 save file. If you never played Mario Kart 7 then characters and parts would be the same as the start as in Mario Kart 7. Obviously there would be no bikes, karts or characters from Mario Kart Wii that did not appear in Mario Kart 7.
Since the first two Cups in Mario Kart 6 are made up of a combination of Mushroom, Flower and Star from Mario Kart Wii, they would get new names (undecided). But no course from Mario Kart Wii's Special Cup appears in Mario Kart 7 so that stays the same.
CUP 1 Luigi Circuit Moo Moo Meadows Toad's Factory Mario Circuit