Basically, the MPS6 introduced at the '02 Paris autoshow will be the Mazdaspeed6. The Mazdaspeed6 has been confirmed for production for Europe (sometime in calendar year 2005). I suspect the Mazdaspeed6 will also be offered in the Japanese market (but that's really a guess of mine, no confirmation on that). As of now, the Mazdaspeed6 has NOT been approved for N. America, but they're studying it.
Currently in Japan, there is a Mazdaspeed6 a-spec (or something like that). These are just bodykits designed by Mazdaspeed that are accessory add-ons to the vehicle. In fact, there are these bodykits for the Demio (Mazda2), Axela (Mazda3), Atenza (Mazda6), and RX-8 .
In Japan, Mazdaspeed also offers some performance upgrades, the RX-8 upgrades being the most popular given the nature of that vehicle. But again, just think of these as dealer-installed accessories.
This is a very complicated relationship (and many things are different for each model), but this is the jist of the situation.