The field of ship design if called Naval Architecture. The study of equipment instillation in ships is Marine Engineering. The study of structures that sit on the bottom or things that interact with the ocean that aren't ships is Ocean Engineering. There is a lot of overlap in the disciplines and it is not unusual for a classic trained Naval Architect to do Ocean Engineering or vice versa. Small boat designers frequently will go by the title of Yacht Designer or Small Vessel Designer. While there is no technical difference between a boat, yacht, and ship, there is a general feeling that ships are large. I am personally not a fan of the "ships carry boats" method of distinguishing between them. There are ships called heavy lift ships which can carry much larger vessels. And some boats wouldn't ever really be carried around on a ship, tugboats for example. Its really not important what they are called, the important thing is that they float, if that's the intent, and are able to complete the mission they were designed or hired for.
Under Graduate Naval Architecture Schools:
University of Michigan: Naval Architecture and Marine Engineering
Virginia Tech: Ocean Engineering
Virginia Tech: Aerospace and Ocean Engineering
University of New Orleans: Naval Architecture and Marine Engineering
United States Naval Academy: Naval Architecture and Ocean Engineering
United States Merchant Marine Academy: Marine Engineering Systems, Naval Architecture Track
Certificate Programs:
Westlawn Institute of Marine Technology
Masters Programs: