An Epidemic Disease is a disease that spreads throughout a large portion of the world. Epidemics tend to be widespread and difficult to stop or control; they affect a large portion of the population, and are not confined to a specific region, habitat, or demographic. Epidemic diseases have included the Black Plague, Smallpox, HIV/AIDS, and the common influenza virus; flu warrants additional information, since it mutates every year and affects a large portion of the population, and so it is a true epidemic disease.
An Endemic Disease is a disease which is confined to a specific region or population demographic. While the endemic disease may be consistent and recurring, it does not spread out of control, nor does it affect a significant portion of the population. Instead, it affects a small number of people on a consistent basis . Examples of endemic disease include Malaria, Cholera, and Dysentery, as well as regional mutagenic or birth disorders caused by region-specific issues.
The difference between the terms is grammatical as well as defined.