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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 definition of fleet is something that moves swiftly. An example of fleet is someone who can move quickly or is very nimble. A fleet is defined as a group of ships, vessels or vehicles that operate together or that are under the control of one person. An example of fleet is a group of ships.