Generally speaking, an armed ship is called a warship. A specific ship that fits the description of a warship is the aircraft carrier named the USS Abraham Lincoln.
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When it was first formed it did not own a ship of the line and had no ship building capacity. Not even an armed merchant fleet was available, It was a Navy in name alone.
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The Portuguese man o' war got its name because its gas-filled bladder or sac resembles a 18th-century Portuguese warship at full sail. This species is not a single organism, but a colonial organism made up of specialized individual polyps working together.
An armed merchant ship, built in Amsterdam in 1628. Shipwrecked on her maiden voyage of the coast of Australia
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The name of the armed services of the Third Reich was Wehrmacht.
It is a privateer, provided it is commissioned or authorised by a Government (usually in time of war). Otherwise, it may be classed as a pirate or buccaneer.