I wouldnt classify a plate coral or a mushroom as having polyps. I wont see hammer, frogspawn or torch as having polips either.
Leathers or other soft bodied corals have no skeliton so to speak of but instead has a very fleshy body mass that is inflated with water to maintan shape.
SPS corals lay down a skeliton base and the individual polyps live inthis base. Gorgonians have a mix of skeliton and fleshy base that the individual feeding polyps extend out of.