Leisure tourism is as it sounds... for leisure purposes only! You go to a resort, or a new city to either relax or visit the sites.
Health tourism usually focuses around a medical treatment. In addition people fit in time to enjoy the sites and relax/recuperate in a relaxing environment. Health tourism combines the medical with the leisure.
For Example: Many people receive fertility treatments in Istanbul and go site seeing in the historic city at the same time. A lot of U.K residents are going to Cyprus, where there are great beaches as well as hospitals that meet international standards for fertility and cosmetic procedures.