I'm not sure if its been brought up but Peter must have copied Adam's regen power.

So if Adam's power of regen is any different than Claire's, Peter has that as well now.

Yes, it would follow that he does have it, if it's different.

But, as I understand it, it's the same as Claire's.

Claire has cellular regeneration.
Adam has constant cellular regeneration.

Claire's power allows her to heal injuries immediatly, but as Adam's cells are regenerating all the time, he can never get old.

But, if I'm remembering correctly, Angela Petrelli stated that after a certain number of times regenerating, the power "evolves" to stop physical aging, but the original power is "cellular regeneration".

I don't think there's really a difference between Claire and Adams regeneration abilities.

If Claire can heal rapidly, it would make sense that her cells are also being formed quite rapidly, making it basically the same as Adams.