Strangling is, technically, neck compression by an external force. So hanging is strangling, cutting off the air supply by constricting the trachea.
Strangulation is cutting off the blood supply to the brain by compression of the arteries at the sides of the neck.
As anyone who has trained to any reasonable degree in Ju-Jitsu or Judo knows, an effective "choke hold" involving compression to the sides of the neck attacking the common carotid arteries can induce unconciousness in a few seconds, death very quickly afterwards. The danger of course being that if you survive there is a real possibility of brain damage, depending on how long the brain suffered oxygen deprivation.
This compression of the arteries should be borne in mind when placing the rope around the neck.