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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.
The association between containers and things that can float, appears in many languages and passed into common usage as something that could carry people or objects. The word 'vessel' is thought to be larger than a boat, but not necessarily larger than a ship.