In Iron Man 3 we see that the Mandarin (who runs the ten rings) is actually an actor hired by Aldrich Killian. Is this a spin off of the ten rings in Iron Man, or did Killian start this one too?
Killian did not start the Ten Rings terrorist group seen in the original Iron Man. Rather, in coming up with ways to cover up the failed Extremis experiments, Killian and the A.I.M. think-tank settled on using terrorist bombings as cover, co-opting the Ten Rings icons to sell the ruse.
The Marvel One-Shot: All Hail the King released with Thor: The Dark World specifically deals with the real Ten Rings breaking the fake Mandarin from Iron Man 3 out of prison so he can meet the real Mandarin.
According to Drew Pearce, co-writer on Iron Man 3 and writer/director for the aforementioned One-Shot:
I actually just felt like it was in the lineage of the information we already dolled out in the movies. In the first movie there was the Ten Rings and in the second movie there was a deleted scene where the rings appear again, and in the third movie we were quite clear in the movie and in the press that there was a mantel that had been co-opted by Killian – partly because if we hadn’t said that it would have completely invalidated a huge part of the first movie which is Raza works for The Ten Rings.