To carry up to six passengers on a non-inspected vessel, an OUPV (Operator of Un-inspected Passenger Vessel) will suffice. This is also known as the "Six Pack" license.
To carry more than six paying passengers on inspected or non-inspected vessels requires a Master's license which determines, by tonnage, what size vessels a person may "captain". These are 25, 50, 100, 200, 500 through unlimited tonnage (large ocean going). Also, based on where your experience is gained, a master's license may be issued as near coastal (inside 200 nautical miles). Voyages outside the US to any foreign port requires other endorsements, primarily STCW (Standards for Training, Communication and Watchstanding)
Most insurance companies require a licensed master for the larger yachts. Hired crews have appropriate licenses for the size yacht they are operating.
I have a 100 ton Master's License and hope to upgrade to the 1600 ton next year. The sea service requirements and training requirements are pretty substantial once you go over 500 tons.