Health science is the disciple of applied science which deals with human and animal health. There are two parts to health science: the study, research, and knowledge of health and the application of that knowledge to improve health, cure diseases, and understanding how humans and animals function.
Medical science is the dealing with the maintenance of health and the prevention and treatment of disease.
I’d say, health science is more of the research part of medicine, and medical science is the actual diagnosis and treatment of the research.
A scientist studying how to cure cancer would you health science, and a doctor working to extinguish cancer from a patient would use medical science to diagnose and treat the patient. (I used extinguish because cancer has no cure, yet ;))
Hope this helps and good luck with your school! :)