If the Coast Guard boards your boat, one of the first questions they'll ask is "Who is the Captain?" In asking that question, they are not trying to determine who knows the most about seamanship. They want to know who is in command of the boat, because, if they are going to cite anyone for a violation, that's the person who is going to get the ticket, even if he is the least skilled person aboard.
This illustrates the difference, within itself, that there is certainly a difference between the position one may hold (eg boatswain, helmsman, planesman, quartermaster, messenger, etc) and the title
one might apprpriatelly place on his/her business card (eg Esq, Capt, Dr).
"Even if he is the least skilled person aboard" certainly points to the fact that the Coast Guard does not grant the title of Captain to every individiual they attempt to identify as the captain of the vessel they have boarded.
The position of captain and the title of Captain are too different things. I might be captain of this yacht. I am not, however, Captain Matt. If anything I'd be Matt, Captain.
While we're definining the word ... captain is not defined as the commander of _any_ vessel. Captain is defined as the commander of a merchant vessel. There are other definitions but that is the one relating it to command of a ship/boat. No, the dictionary doesn't even grant the title to a yachtsman.
You might be the captain but unless you have been commissioned as such you are certainly not a Captain, or "Captain Umptysquat". Holding the position does not grant the title.