X11 and C11 use the same hashing algorithms, just in different order. Afaik, both were independently developed around the same time.
FWIW, I can confirm that you are correct on both calls. The difference is that Skein512 is the
fourth link in the x11 chain and the
sixth link in the C11 chain.
I'm still trying to work out whether this difference in ordering is responsible for the wide-ranging experience of cooler running and reduced power consumption with x11 that somehow mysteriously fails to accompany C11.
It's a funny old world.
Cheers
Graham