The cervical vertebrae is the only thing that holds their head up. It also houses the spinal cord. The spinal cord houses the nerves that go to all areas of the dog's body. Any prolonged pulling or sudden force can cause temporary and possible permanent misalignment of the vertebrae.
This misalignment can impinge the nerves that go to the front legs, which can result in abnormal sensation or numbness in the forelimbs. Sudden force can also cause a whiplash-like injury.
Collars can cause or exacerbate many physical conditions. Pulling on the neck puts pressure on several different areas such as the trachea, possibly causing trachea collapse, the lymph nodes which can have negative effects on the lymphatic system, arteries and veins which can lower blood flow to the eyes and brain, and the thyroid gland which can cause issues with thyroid function.
Not to mention the skin and fur beneath the collar that can be bruised, show hair loss or if not fitted properly, can cut into the skin of the dog’s neck.
Some collars can cause more severe issues, such as choke chains and prong collars, but they all put pressure on the same parts of the neck. And can cause the same types of injuries to the dog. Obviously, the choke chain can also cause lack of oxygen going to the brain, as it does what its name says, chokes the dog. The more pressure put on the dog’s neck, the more severe the injuries can be.
So why do these collars appear to work? It’s simple, the dog realizes that it causes them discomfort and pain and they learn to avoid the pain by not pulling.