It depends how you count them, but there are probably hundreds of different string models which differ in the particulars of how they obtain standard-model leptons.
It helps to be clear what the standard model is. It's a set of chiral spin-1/2 fermions, that interact with various gauge bosons and with a Higgs field that has a nonzero vev. There is an overall symmetry group, and each quantum field transforms in a particular representation of that symmetry group, and the representations determine the interactions.
So you basically need there to be gauge symmetries, and spin-0, spin-1/2, and spin-1 objects with the necessary transformation properties. And the strings and branes of string theory generically produce such objects; so it's "just" a matter of finding the right recipe of extra dimensions, fluxes, and symmetry-breakings, so as to specifically produce the standard model.
But exactly how it works is different in heterotic string theory, Type I/II string theory, M-theory and F-theory. Another salient difference is whether you start with supersymmetry and then break it, and whether you start with grand unification and then break it (which is the usual way), or whether you try to start directly with a non-susy and non-unified model. Still another unusual (but not unknown) option is for the standard-model fields to be composite rather than elementary.
This is an interesting topic and I don't mind talking about it, but there are too many options to just sum up everything. Meanwhile you can find more by looking for "string phenomenology".