HMS Pelican was sold in 1763 and so its Royal Navy crew, including the officers would have been paid off and free to find other ships, either Naval and merchant, in which to serve. If the Navy didn't immediately have another command for him or he lacked the right patronage, he would have gone on half pay and might certainly have become the master of a merchant ship. However there was an HMS Pitt which was purchased by the Navy in 1763. It was an 8-gun cutter that foundered in the Atlantic in 1766, "coming from Africa". (source Wikipedia).
HMS Pelican (1757) was a sloop which would have been commanded by a Commander, whereas the Master might have been the navigator, effectively the second in command. Naval Captains commanded much larger ships. I don't think the terminology of command used on civilian ships was so precise.
1766 was of course the height of the American War of Independence (also known as the American Revolutionary War), so whether the Pitt he was commanding was civilian or Navy, it may well have been supporting the Royal Navy.