An infectious disease is a disease caused by a microorganism and therefore potentially infinitely transferable to new individuals. It may or may not be communicable. An example of a non-communicable disease is disease caused by toxins from food poisoning or infection caused by toxins in the environment, such as tetanus.
A communicable disease on the other hand is an infectious disease that is contagious and which can be transmitted from one source to another by infectious bacteria or viral organisms.