Zermelo's system does diverge from the theory of types in others of its axioms. There are Zermelo's axioms of power set, pairing, Aussonderung, sum, extensionality. Zermelo did not depict his system as disposed in types. Zermelo owned to a few additional axioms. There was the axiom of choice, which he originated and counted in, and an axiom of infinity. Zermelo's actual system was complicated by the distinction between class and individual. Zermelo's protections against the paradoxes consists essentially in eschewing too big classes. There is no class of everything(stl272)
Zermelo's natural numbers and von Neumann's have the great advantage over Gottlob Frege's of requiring no axiom of infinity(stl282)
For the assurance that classes fail to exist only if they would be bigger than all that exist, there was only very partial provision in Zermelo's schema of Aussonderung. Full provision was added rather by Fraenkel and Skolem in the axiom schema of replacement(stl284)
Zermelo's system in its main outlines came of the theory of types by the switch to general variables and cumulative types. The alternative departure from the theory of types that suggests itself is this: that we reconstrue unindexed variables as truly general variables (rather than as typically ambiguous)) but yet keep the restriction that the particular formulas put for 'Fx' must be stratified. Such is the system called "NF"(stl287)