Presumption — a proposition that must be true if an argument is sound, though not explicitly stated in the premises.
Implication — a proposition that cannot be false if an argument is sound, though not explicitly stated in the premises.
Begging the question (or petitio principii) — an informal fallacy where an argument presumes, implicitly or explicitly, its implied conclusion in the premises.
Lee,
For what it’s worth, I don’t regard question begging, i.e., petitio principii, as a fallacy at all — informal or otherwise. I think the whole idea that there’s a fallacy is itself an artifact of justificationism. The real problem people have with it is that it does not provide the simulacrum of a justification. Naturally, this bothers justificationists. So they decided that it’s a fallacy — of some sort or another. Of what sort they’re not exactly sure, since they take in justificationism with their mother’s milk and have never considered living without it.