The archaic word for a 'ship' is an 'ARK', as in 'Noah's Ark, or H.M.S. Ark Royal, the Royal Ship. A 'ship' has technically three (3) masts, a foremast, a mainmast and a mizzen mast. The only modern ship to technically have three masts was 'H.M.Y. Britannia', now decommissioned.
In modern terms a ship can be thought of as any floating vessel that has a mechanical means of propulsion (and engine and propellers). Boats require natural propulsion such as rowers or wind(sails).
However, the differences can be very subjective, because you can have motor boats and sailing ships.