Boat, vessel, ship, craft are comparable when they denote a floating structure designed to carry persons or goods over water.
Boat is sometimes used as a general designation of such a structure but more specifically it is applicable to a small, typically open structure operated by oars, paddles, or poles.
Vessel suggests a purpose as well as a form, the term in general applying to anything hollowed out so as to serve as a receptacle. Hence, vessel is appropriate when the containing and transporting of goods and persons is stressed; it is applied chiefly to large boats, especially seagoing boats, in the business of carrying passengers or freight or serving as a base of operations at sea (as in fishing or in war).
Ship is the preferred term for the large seagoing vessel, especially when its navigation rather than its business is emphasized.
Ship also suggests more personality, more romance, and more beauty than the other words and therefore is far more common in poetry and in figurative use.
Craft may be used as a singular or collective noun and is now applicable to any type of boat or ship that plies the water.
Originally it was found only in the phrase small craft and was applied to smaller vessels, especially to those in the service of ships (as lighters, tugs, and fireboats) or to those forming part of a navy or fleet.
The word may still be used in the sense of small craft but it tends to become a comprehensive term covering all kinds of boats and vessels.
As a singular, craft unqualified is often a vague and general term.
However, for that very reason, craft is often, when it is qualified, a better choice than boat, ship, or vessel.