Hi, Shadae, One of these is a specialty within the mental health treatment world, while the other is a level of therapist. Let me explain:
A family therapist is a therapist who specializes in family treatment. This person must have at least a master's degree in social work, counseling, or clinical psychology and a license by the state to treat people and bill insurance for that treatment.
A psychologist is someone with a doctorate in some aspect of psychology, who may choose to use that to get a license and treat people as a therapist (including a family therapist), or they may use it as a college professor, a researcher, etc. People with their master's degrees are not "psychologists." They are called counselors, social workers, therapists, etc. Only if they go on to earn their doctorate in psychology do they then change to the term psychologist.
So a family therapist COULD also be a person with a doctorate in psychology, and would therefore be a psychologist, too.
Every state has unique therapist licensing processes which graduate schools in that state will prepare you for in terms of your coursework. If you go to grad school in one state and plan to practice in another, be sure to look up the other state's requirements so you get what you need to be qualified. Then some states have an initial license and a higher level license - the higher one you get after so many hours/years of documented experience, and that's typically the one that allows you to bill insurance as an individual practitioner (e.g. go into private practice).
Let me know if this helps clarify!