That's an interesting question with no very good answer. The sea has a complex terminology all its own, and the more you get into it the richer and more complicated it gets. I think I'm just going to cheat and consult a dictionary. Otherwise I will just get tangled up trying to remember the differences between pinnaces, yawls, schooners, dinghies, cutters, ketches, and Chesapeake skipjacks.
ahdictionary.org says that a boat is
a. A relatively small, usually open craft of a size that might be carried aboard a ship.
b. An inland vessel of any size.
c. A ship or submarine.
According to (c), "boat" CAN mean "ship," which makes perfect sense. The "ferryboat" we took across Lake Michigan was the S. S. Badger, a 125-meter, 4000-ton coal-burning steamship, complete with staterooms.
I learned something today, because the idea that a boat means something that "might be carried ABOARD a ship" was something I didn't know, but it makes sense.
Again according to the dictionary, a "ship" is
a. A vessel of considerable size for deep-water navigation.
b. A sailing vessel having three or more square-rigged masts.