Is there a difference between Euler systems and Kolyvagin systems - or do they refer to the same thing? For example there is the Heegner point Euler system, but you don't really see a Heegner point Kolyvagin system.

Also, Rubin-Mazur prove that the space of Kolyvagin system is free of rank one (under certain conditions) - is something similar true for Euler systems?

In particular I would like some clarification on Mazur-Rubin "Kolyvagin Systems" Section 3.2 (e.g. in Theorem 3.2.4 what do these technical assumptions really mean)