A psychologist has a degree in psychology (the study of the mind). Psychologists may or may not be therapists. Those who do therapy are known as Clinical Psychologists. Other psychologists are engaged in research and a variety of other pursuits.
A therapist has special training in ways of helping clients identify and deal with behavioral and emotional issues. Therapists may be psychologists, Social Workers, or have other training. Most psychiatrists, who are also medical doctors, practice therapy.
The essential characteristics are training and hours in the field. Before licensing (or certification, in some cases), all therapists are required to have thousands of “contact hours,” where they work with clients under the supervision of a licensed therapist. In addition to contact hours, a certain number of hours of formal training are required (often received as part of their college work), and they must also pass a comprehensive licensing examination.
Addiction therapists (often called “Addiction Professionals”, or “CAPs”) have additional specialized training and experience in dealing with issues surrounding alcoholism and addiction to other drugs. They may or may not be recovering themselves. However, in my personal opinion, it “takes one to know one.”
I do not recommend dealing with unlicensed “therapists,” regardless of who they are or what experience they claim. This especially applies to some clergy, who may be allowed to practice, by law, without having the requisite training to do a competent job. Always ask to see a state-issued license that specifically pertains to addiction, such as Certified Addiction Professional, or refers to something like Licensed Mental Health Counselor or Licensed Clinical Social Worker, or a counselor affiliated with a licensed treatment facility.