I think sedevacantist believe that the poep exists, just that he may be excommunicated. Most sedevacantists today seem to believe that the pope legally holds the office, but not morally.
The sede vacantists I associate with these three actually believe the seat is vacant, i.e. no Pope. They do not even accept the Pope at all, as if he were a representative of a different religion than their own. Those I know personally who gravitate to these three emphatically reject any possibility of the existence of who claims to be the Pope in Rome in their eyes.
At least one priest and one bishop in close communion with these three insist they are NOT sede vacantists, but one explained to me they believe a Pope sits in the chair, but more like an empty suit or a corpse propped up there. I have heard the descriptive term sede privatist used in this case. Although these insist they are NOT sede vacantists, they can be described as having never met a sede vacantist they didn't like.
Those I have known whether from Monroe, Albany, Cincinnati, or the seminary are the sede vacantists I describe.
I met Fr. Dardis who is mentioned in the other thread and who disputes Fr. Cekada,
http://www.freerepublic.com/focus/f-religion/1393366/posts?page=49#49 while outside of Terri's room as she lay dying inside. He stood out from the rest, being the only priest in a true cassock and impressed me greatly with his priestly countenance.
As you may gather, I am not a sede vacantist at all, and am at odds with those who are. I am a plain traditional Catholic.