According to Varieties of Faith, Sheogorath is born when Lorkhan's divine spark is removed. I read somewhere that Sheogorath is Lorkhan's creativity or madness. So Sheo is just an aspect of Lorkhan. Does that mean that If I mantled the one, I would also be mantling the other?
It's a bit more complicated than that but it is made clearer (or was) once we were told that Jyggalag is Sheogorath. See the guys who phrased it that way were working on limited info. They noticed Sheogorath wasn't there before Lorkhan, cool. They made the connection that Lorkhan had to be there for Sheogorath, also cool. However, people thought Jyggalag was just a ridiculous name by a troll scholar.
The point of Mundus was to allow free will and eventual transcendance for Lorkhan, accidentally (or purposefully, depends who you ask) giving it to everyone else. As one of the aspects of "Order" as shown by Jyggalag is causal determinism (different from Hermaeus Mora, god of fatalistic determinism), that everything that will ever happen in the Aurbis can be predicted by tracing cause and effect with algorithms and equations as though people were just numbers, his existence hinges on the lack of free will to resist or to make unexpected decisions. Sheogorath is what happens when free will happens, Jyggalag, his main function impossible, goes mad.
So while Lorkhan and Sheogorath are intimately and inseparably related, one is not the other.