What is a large ship with sails called?

Sailing ship is a sea-going vessel that uses sails mounted on masts to harness the power of wind and propel the vessel.

Does this include the 3 types of sails?

Headsail: The small sail in front of the mast, attached to the mast and forestay. Specialty sails: Any special utility sails, like spinnakers - large, balloon-shaped sails for downwind use.