I believe they make a OEM Corsa for the 1000RR, not just the Repsol edition but all of them. I saw a brand new 1000RR, last year so this was the '04 model, black, with a set of Corsa's on it at one of the local dealerships.
Just like Bridgestone and other tire makers you have a choice of going OEM (tires they put on the bike at the factory) or getting the off the shelf versions (not specifically designed for any bike).
The argument, as I understand it, is that the OEM versions are supposed to be designed with that particular bike in mind (obviously). It's supposed to improve or 'exploit' the handling characteristics of that specific bike model.
The other side of that argument is that the off the shelf/non model specific tires are supposed to be stickier than OEM. I did the comparo myself, sort of, I used a friend's BT010 OEM take off from his bike, still had lots of tread left after I picked up a nail in my BT010, off the shelf version. Not sure if it was just a mental thing (thinking about above mentioned argument while riding). But the OEM tires did seem to break loose easier coming hard out of turns. Of course they were not mounted on the bike they were originally intended for.
I just usually buy the regular tires and skip past the shoes designed for my specific model. No complaints.
Never heard anything about the Strada's??