The laws governing both carrying and operating a marine radio station aboard all vessels including boats and yachts are not really complex. The difficulty is in knowing which of the various U.S. and International organizations govern and in which circumstance.
While all boaters should know and understand the rules of their nation state, the reality is that the average boater is generally interested in only (2) aspects of the law:
Even though there are a number of organizations that contribute to these laws, the (2) big international players are:
The ITU, a UN agency, coordinates the international use of the radio spectrum among member states.
The IMO regulates the outfitting and operation of most vessels engaged on international voyages, except warships.
Additionally each nation state has their own governing bodies: In Australia it is the Australian "Communications and Media Authority" (ACMA), Bermuda the Ministry of Environment, Telecommunications and E-Commerce (METEC), Canada has Industry Canada, New Zealand has Radio Spectrum Management (RSM), the UK has the "Office of Communications" (Ofcom), and the US has the "Federal Communications Commission" (FCC). Many other organizations within each nation state provide support and assistance to these primary organizations.
A good example of these supporting organizations in the United States, would be the U.S. Coast Guard (USCG.) The FCC regulates all sales, marketing, technical specifications, and use of radios in the U.S., including those onboard any recreational, commercial, state and local government, and foreign vessels in U.S. territorial waters. The USCG regulates which vessels are required to carry radios; most commercial vessels, foreign vessels in U.S. waters, survival craft, and vessels subject to the Bridge-to-Bridge Act (generally all vessels over 20m length.) and certain vessels operating in a Vessel Traffic Service (VTS) area.
So, in general terms this means that we can ignore the ITU, since the FCC regulations must fall within the ITU regulations with rare exception; and the IMO only comes into play if we are on an international voyage or communicating with a foreign radio station. This leaves the FCC and the USCG as the largest influencing organizations on U.S. boaters.
Simply put, the FCC regulates the use of radios in the U.S. and the USCG regulates which vessels are required to carry them.