A warship is a ship built for fighting — it carries guns, missiles, or aircraft, and belongs to a country's navy. It is one word, not two, and it is countable: one warship, three warships.

"Warship" is the general word that covers many kinds: a destroyer, a frigate, a submarine, an aircraft carrier are all warships. So you use it when the exact type does not matter, or when you do not know it. News reports use it a lot for exactly that reason — "three warships entered the area" tells you enough.

Notice that it does not mean "a ship that is in a war right now". A navy's warships are warships in peacetime too; the word is about what the ship is built to do, not what it is doing today. Cargo ships and passenger ships are not warships even if a war is happening around them.

The word feels a little more formal and more written than spoken. In casual talk people are more likely to say "a navy ship". "Battleship" is not a synonym either — a battleship is one particular huge, heavily-armed type, and no country really uses them any more, though the word survives in the board game.