Many (most) physicians who do research also provide clinical care. They most often do an internship and residency and then learn research skills within in a subspecialty during a fellowship. Most often the fellowship includes patient care as well as research.
There are some fellowships with a research focus for those who choose not to become licensed to practice medicine but those are very rare and it is the rare medical school graduate who wants to close the door to ever caring for patients.
During a fellowship, the fellow is often writing grant proposals that, if funded, will provide partial salary support after the fellowship is completed. A physician/researcher will often be on the payroll of a medical school or pharmaceutical company. The people in pharm may not have any patient care responsibilities but those in academic settings bring in money through patient care, research grants, and also support the educational activities of the medical school through lectures and/or bedside teaching and the supervision of medical students, residents and fellows in clinical settings.