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Vessel is a catch-all term, like 'watercraft', which describes any floating object used for the carriage of people or goods. Generally smaller and less complex vessels are 'boats', whilst larger and more complex vessels are 'ships'. As a general rule, you can put a boat on a ship, but you can't put a ship on a boat.
A vehicle (from Latin: vehiculum) is a mobile machine that transports people or cargo. Typical vehicles include wagons, bicycles, motor vehicles (motorcycles, trucks, buses), railed vehicles (trains, trams), watercraft (ships, boats), aircraft and spacecraft. Land vehicles are classified broadly by what is used to apply steering and drive forces against the ground: wheeled, tracked, railed or skied. ISO 3833-1977 is the standard, also internationally used in legislation, for road vehicles types, terms and definitions.