No they aren't mutually exclusive. Vouchers could be made usable at charter schools and are in some places, for all I know. But vouchers are superfluous in the context of charters. Charters don't charge tuition, as far as I know. They are reimbursed by the Gov for their students. Schools accepting vouchers would have to be licensed by the Gov too. One crucial difference is whether voucher schools are allowed to levy tuition surcharges. Another wrinkle is the jurisdiction in which the voucher or charter school is available. If the regions are identical and there is no surcharge, then vouchers and charters are identical.
The other difference is that vouchers originate as rights assigned to a handful of students who then have a choice of existing schools, perhaps including private ones, depending on the local scheme. By contrast, a charter school is organized from scratch and opened for business.
A crucial cost advantage for charters relative to pre-existing schools, whether or not the latter accept vouchers, is they can start with younger teachers and save a bundle in the near term on salary. Labor cost is roughly 80% of school cost.
The basic common feature of charters and vouchers is that choice affords previously unavailable opportunities for some, but the resulting sorting of students goes against the grain of equality.
There's something to be said for a better-functioning meritocracy, but in this vein kids are hostage to their parents' merit. More broadly, I'd say the more basic problem is not that people fall into the wrong social class, but that we have social classes in the first place.
mbs