Dhabihah is the method, not just the animal. A sharp blade cuts the throat in one continuous stroke, severing the trachea, the esophagus and the jugular veins and carotid arteries, so that the blood, which is itself forbidden as food, drains from the body before the meat is handled further. The slaughterer invokes the name of God over the animal, and classical law requires the slaughterer to be a Muslim or, in most schools, a Jew or Christian, on the reasoning that the food of the People of the Book is generally lawful to Muslims.
Mechanized slaughter and the modern halal certification industry have made the details contested rather than settled. Disputes among contemporary scholars and certifying bodies concern whether stunning before the cut is compatible with the requirement that the animal be alive at the moment of slaughter, and whether machine cutting satisfies the requirement for an intentional, named act performed by a person. Certification bodies differ by country and by school of law, and no single global standard governs the label.
The same method, applied to the same animals for closely related reasons, underlies Jewish shechita; the two traditions differ mainly in who may perform the cut and in the blessing or invocation that must accompany it.