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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.
Ship and boat - can be used interchangeably, but a ship is usually a large sea-going vessel, a boat is usually a small open vessel (though apparently in the USA boat can also mean a large sea-going vessel, just to confuse matters!). Ferry - a boat used to carry people, vehicles and good across a stretch of water.