No it's not a silly question at all
Sedevacatists typically doesnt, but SSPX does. That being said the SSPX isnt sede. They believe that Francis is pope and they pray for him in the eucharistic prayers in each and every mass the celebrate. They refuse to accept two of the documents from Vatican ii concerning the church's view on interreligiousity (Nostra aetate) and human dignity (DH) and thus they've been subject to much frustrations within the Vatican.
They dont celebrate Novus Ordo or the new mass as people call it. They only celebrate the Traditional Latin Mass. They consider themselves to be a fraternity much like any other, but because of their arguments with the Vatican Pope John Paul ii decided not to grant them disposition to ordain new bishops.
Without bishops the SSPX would in time cease to exist which was the game of the pope, or at least willed by him. As time went by Archbishop Marcel Levfebrve came down with illness and shortly before approaching death he decided to disobey the pope and ordain bishops himself. This action triggered an automatic excommunication and made them schismatic.
This has later been lifted by pope Benedict XVI and now they're in a irregular communion with the church.
SSPX on their site stresses that they never left nor departed from the church in any way other than the the ordination of the bishops against the will of JPii.
Soooo, the SSPX is reverent and pious Catholics whereby Sedevacantist typically aren't.