Right, Pax, but not only that, but even if we grant the validity of his distinction, those with the votum are merely subset of those with a generic desire. You cannot have a votum for Baptism without also the natural "desire" for it. Oh, wait, check that, perhaps a Hindu in Tibet can somehow have this infused magical votum while never actually desiring Baptism. Of course, even that is based on their natural "desire" to do everything God wants. Yet the Pope says that EVERY SINGLE ONE of those is lost, including those among the "desirers" who happen also to have the "votum". Otherwise he would simply say "some" or "most" of them are lost.
Really the reason the Pope uses the Latin "desire" is because the term "votum" hadn't been introduced yet (this is an early docuмent). It does NOT mean "only natural desire" but is a broader term.