There seem to be two definitions of what a saturated class should be:

1. A class of morphisms closed under retracts, pushouts and transfinite composition.
2. A class of monomorphisms containing all isomomorphisms, closed under retracts, pushouts, arbitrary coproducts and countable composition.

My question is, does it make a difference which definition one choses in the context of the cofibrantly generated modelstructures on

• $\mathbf{Top}$, with respect to the Quillen model structure
• $\mathbf{sSet}$, with respect to the Quillen (or Kan) Model structure
• $\mathbf{Cat}$, with respect to the Thomason model structure