An addiction medicine specialist is a doctor who treats patients with addictions to substances like drugs and alcohol or, in some cases, behaviors like gambling. Many of these specialists also treat the diseases that stem from these addictions.
These physicians are specially trained to prevent and treat the disease of addiction via psychiatric means, or other fields of medicine like family or internal medicine.

A physiatrist is a doctor who specializes in the rehabilitation and physiological treatment of patients with an illness or injury that affects movement.
These specialists have extensive knowledge of the nerves, muscles, bone, and brain. Physiatrists are also experts in pain medication.
Some common conditions that physiatrists treat are rheumatoid arthritis, neurological and spinal disorders and injuries, chronic pain disorders, like fibromyalgia, and musculoskeletal issues, like broken bones and torn muscles.
These physicians also often coordinate a team of other specialists in order to maximize the patient's recovery, such as occupational therapists, speech therapists, neurologists, orthopedists, and counselors.

Anesthesiologists are physicians who are trained to administer anesthetics, which are medicines used to block nerve sensation. Anesthesia can be either local to one specific part of a body, like a tooth, or regional to block feeling to a larger portion of the body, such as during an epidural for child birth. It can also be more general to block sensation to the entire body, resulting in unconsciousness.
Anesthesiologists assist in surgery by determining how much anesthesia is necessary and by monitoring the patient's level of responsiveness and vital signs throughout the procedure. The anesthesia specialist will also bring the patient out of anesthesia and then continue to monitor his or her vital signs post-operation.
Besides assisting in surgeries, anesthesiologists may also treat patients suffering from chronic pain.