All three of these terms refer to the person in ultimate charge of a vessel. Every person in overall command of a vessel is the Captain of that vessel; although on some, usually large, commercial, sea-going vessels they will be referred to as the Master. They will typically be a licensed Master Mariner.
A Master Mariner (MM) is someone who has an unrestricted Captain’s or Master’s license, usually from the flag state in which the vessel is registered; meaning they are allowed to be in overall charge of almost any size or power of vessel, anywhere in the world.
The often heard term Skipper is of course just a nickname for the Captain. It tends to be used to refer to the Captain of a smaller boat or yacht, or in say fishing vessels, where the Captain is often a friend or relative of the crewmembers, as well as their boss. In most of the world’s English-Speaking Naval Forces the person in overall charge of the vessel is the CO or Commanding Officer, but when aboard he too will generally be referred to as Captain.
In short, if you are unsure how to refer to the person in charge of a particular vessel it is safest to refer to them as the Captain.
(Image Credit: Sint Smeding)
(Image Credit: Sint Smeding)