Odysseus Overcome by Demodocus' Song
, by Francesco Hayez, 1813–15
The Greek μυθολογία [mythología] ("story," "lore," "legends," "the telling of stories") combines the word μῦθος [mythos] ("story") and the suffix -λογία [-logia] ("study"). Plato uses [μυθολογία] as a general term for "fiction" or "story-telling" of any kind. The Late Latin mythologia, which occurs in the title of Latin author Fulgentius' fifth-century Mythologiæ, denoted the explication of Greek and Roman stories about their gods, which we now call classical mythology. Although Fulgentius' conflation with the contemporary African Saint Fulgentius is now questioned, the Mythologiæ explicitly treated its subject matter as allegories requiring interpretation and not as true events.
Borrowed from the Middle French mythologie, the English word "mythology" first appeared in the fifteenth century.  From Lydgate until the seventeenth or eighteenth-century, mythology was used to mean a moral, fable, allegory or a parable, or collection of traditional stories, understood to be false. It came eventually to be applied to similar bodies of traditional stories among other polytheistic cultures around the world.
The word mythology entered the English language before the word "myth"; Johnson's Dictionary, for example, has an entry for mythology, but not for myth.  Indeed, the Greek loanword mythos (pl. mythoi) and Latinate mythus (pl. mythi) both appeared in English before the first example of myth in 1830.