An important thing is a whenever discussing a vaulted type ceiling most people kept in mind that a valuated ceiling and cathedral ceilings are the same.
As the name suggests Barrel vaulted ceilings mean creating a tunnel or barrel kind illusion on the ceiling area. The Barrel vaulted type ceilings are in a semicircular arch and round jutting into the space.A Groin Vaulted Ceilings are created by an intersecting of two-barrel type vaults. So that groin ceiling is generated in a square shape with a point in the central part of the ceiling area.
