Warship

A warship is any vessel, whether on the ocean or in outerspace, built explicitly for combat. They are heavily armed and armored.

Star Trek

Most Federation Starships in the TNG era of Star Trek are not true warships, desipte their armorment. They tend to serve multiple functions including exploration, scientific research, diplomatic negotiations, transports in addition to being the Federation's front line of defense. This is in stark contrast with TOS where the ships tended to be more focused just on defense and exploration.

It appears that with their alliance with the Klingons and silence from the Romulans for so many years, the Federation felt they no longer needed such a high level of military presence. With the increased threats of the Borg and Dominion, the Federation has realized that they are not as safe as they thought they were and have once again built starships explicitly for combat, such as the Defiant-class

Star Wars

The Galactic Empire has many classes of warship, including but not limited to the Imperial Star Destroyer and Executor-class Star Dreadnaught.

The ships used in battle by other organizations may or may not be true warships. The "battleships" of the Trade Federation, for example, are converted transports.