Some — but not all — infectious diseases spread directly from one person to another. Infectious diseases that spread from person to person are said to be contagious.
Some infections spread to people from an animal or insect, but are not contagious from another human.
Contagious diseases (such as the flu, colds, or strep throat) spread from person to person in several ways -- including through the air, through respiratory droplets (cough, sneeze, etc), and direct contact either with a person or a surface that had previously been touched by an infected person.