Actually, a good question, and yes, as "shorthand," the supporter of Vatican II and (currently) Francis, would call himself a Papist.
But it occurred to me after I had posted yesterday, that the sedevacantist would respond that he, too, is a Papist -- he just doesn't think that John XXIII, Paul VI, etc. were real popes.
So, technically, they both can be called Papists. OTOH, a sedevacantist would not use the term too often, lest people think it implies loyalty to Francis. But he might use it if the context of his POV was clear.
Good stuff, thanks.