Myth, legend, saga all mean a story which has come down from the past, which ostensibly relates a historical event or events, and of which the origin has been lost or forgotten.
Myth varies considerably in its denotation and connotation depending on the persuasion of the user. Often the word is used to designate a usually fanciful and imaginative story that explains a natural phenomenon or a social practice, institution, or belief.
It is also used to designate a story, belief, or notion commonly held to be true but utterly without factual basis.
The word may be used with wide comprehensiveness in general writing or with narrow exclusiveness and specificity in more limited use.
Legend is likewise used with latitude, but in its most typical use it is likely to apply to a story, incident, or notion attached to a particular person or place that purports to be historical and often has or seems to have a basis in historical reality although as a whole it is either incredible or unverifiable.
Saga may refer to a long, continued, heroic story that is action-packed but not especially romantic, that deals with a person or group, and that is historical or legendary or both.