A Warrior Undead is an undead being (usually a humanoid skeleton, but vampires, ghosts, and zombies also qualify) that uses armour, weaponry, and tactics. This requires some degree of intelligence, or at least muscle memory, as the warrior must be able to remember the skills they possessed in life and still be able to use those skills in their undead form. A brainless zombie who just whacks with whatever they were holding when they died does not count as a warrior undead, but a zombie that still carries the weapon they used while alive and can keep pace with or defeat a trained opponent does.
Fighting styles and philosophies of warrior undead vary. You could see a medieval European knight on an undead horse; an undead samurai that uses dao and a bow, or an undead sharpshooter who retains their now literal dead eye. Some amp up their arsenals with magic, becoming stronger than they were before they died. They are usually evil or Mooks, though some are neutral or on the side of good. On rare occasions, they may even be a mentor or teacher to another (usually alive) character, acting as a posthumous Old Master or a more physical Spirit Advisor. Most revenants are this to some degree.
When at sea or in a port, they're usually a Ghost Pirate, and if a few more things are mixed in they count as a Ninja Pirate Zombie Robot. Compare The Paladin and the Monster Knight. For undead mages, see Our Liches Are Different. Not to be confused with Blood Knight. See Cavalry of the Dead when a character has the ability to summon and control undead warriors en masse. Can be the result of It Can Think when applied to The Undead. Often overlaps with Undying Warrior.