Contagious is defined as "capable of being transmitted from individual to individual (person to person; animal to animal); communicable."
Infectious is defined as "caused by or capable of being communicated by infection." And to understand that you need to know that infection is defined as "1. invasion and multipication of microorganisms in body tissues."
So something can be infectious without being contagious. Cholera and typhoid fever are both termed water- and food-borne infectious diseases. (They are caused by bacteria and spread through contaminated water and food.) So, no, I would not say cholera is contagious, but it is an infectious disease.
Examples of contagious disease are AIDS, influenza, and the common cold, which are passed fairly easily through contact between an infected individual and a susceptible individual.
(Sources: Dorland's Illustrated Medical Dictionary, 30th edition, and Saunders Comprehensive Veterinary Dictionary, 2nd edition.)