Sometimes, The Plague overlaps with The Virus and turns its victims into horrible degenerate mutants. The difference is that The Virus tends to be a sentient entity with a Hivemind, while The Plague is simply a spread of disease acting without malice (although it might have been released maliciously initially).
For artificially and magically created diseases, see Synthetic Plague and Mystical Plague respectively. Compare Depopulation Bomb. The Black Death is a particularly famous case. (In fact, technically speaking the word “plague” refers specifically to the Black Death, aka the bubonic plague, although “plague” is more loosely used to describe any devastating epidemic.)