late 14c., "a communicable disease; a harmful or corrupting influence," from Old French contagion and directly from Latin contagionem (nominative contagio) "a touching, contact," often in a bad sense, "a contact with something physically or morally unclean, contagion," from contingere "to touch," from assimilated form of com "with, together" (see con-) + tangere "to touch," from PIE root *tag- "to touch, handle." Meaning "infectious contact or communication" is from 1620s.
A distinction between contagion and infection is sometimes adopted, the former being limited to the transmission of disease by actual contact of the diseased part with a healthy absorbent or abraded surface, and the latter to transmission through the atmosphere by floating germs or miasmata. There are, however, cases of transmission which do not fall under either of these divisions, and there are some which fall under both. In common use no precise discrimination of the two words is attempted. [Century Dictionary, 1897]