No. The short answer is no, your dentist is not an orthodontist. According to the American Association of Orthodontists (AAO), an orthodontist is an individual who completed college, dental school, and an orthodontic residency.
Only dentists who graduate at the top of their dental class are accepted into a residency program. Similar to any other medical specialist, orthodontists complete their residency program for two to three years after dental school. This means that all orthodontists are dentists, but not all dentists are orthodontists.
An orthodontist has completed both four years of dental school and an additional two to three years in orthodontic residency
The AAO also states that while there is some instruction regarding orthodontics in dental school, it is minimal. It is in the orthodontic residency program that orthodontists receive intensive instruction to learn proper, safe tooth movement (orthodontics) and the guidance of dental, jaw and facial development (dentofacial orthopedics). These extra years of schooling make the orthodontist the dental specialist in moving teeth and aligning jaws.