Shechita (photos here and video here-caution) is the ritual slaughter of mammals and birds according to the set of Jewish dietary laws called Kashrut. The authority for this is the Torah:
"And whatsoever man there be of the children of Israel, or of the strangers that sojourn among you, which hunteth and catcheth any beast or fowl that may be eaten; he shall even pour out the blood thereof, and cover it with dust. For it is the life of all flesh; the blood of it is for the life thereof: therefore I said unto the children of Israel, Ye shall eat the blood of no manner of flesh: for the life of all flesh is the blood thereof: whosoever eateth it shall be cut off." ~Lev. 17:13-17:14
The act is performed by a shoshet who severs the trachea, esophagus, carotid arteries and jugular veins using a chalef and allows the blood to drain out. The prescribed animals slaughtered in this way are labeled kosher.
Dhabihah is the ritual slaughter of most animals, excluding seafood, according to Islamic dietary law. The authority for this is the Qur'an:
"Forbidden for you are carrion, and blood, and flesh of swine, and that which has been slaughtered while proclaiming the name of any other than God, and one killed by strangling, and one killed with blunt weapons, and one which died by falling, and that which was gored by the horns of some animal, and one eaten by a wild beast, except those whom you slaughter; and that which is slaughtered at the altar and that which is distributed by the throwing of arrows [for an omen]; this is an act of sin." ~Al-Maidah 5:3The method consists of using a sharp knife to make a swift, deep incision on the neck, which severs the esophagus, the trachea, and the jugular veins and carotid arteries on both sides but leaves the spinal cord intact, after which the blood is drained. Meat that has met this standard is certified halal.
Although achieved by similar methods, kosher and halal meat are not interchangeable. Both methods of slaughter have been considered by animal rights groups to be inhumane, but the international animal welfare community approves as long as the animal's heard and neck are securely restrained to avoid movement that would result in a poor cut and slow loss of consciousness. In the U.S., the federal government exempted ritual slaughter from the Humane Slaughter Act in 1958 at the request of immigrants. Unlike shechita, which must be performed by a specially-trained holy man, dhabihah may be performed by individual Muslims, some of whom do so at the Wagon Wheel Ranch in Mt. Airy, Maryland, and other farms that cater to this niche market.