Fable

An idle, groundless, and worthless story, like the mythological legends of the heathen and the vain traditions of the Jews. These were often not only false and weak, but also pernicious, 1 Timothy 4:7 Titus 1:14 2 Peter 1:16.

Source: ATS Bible Dictionary
Fable

Applied in the New Testament to the traditions and speculations, "cunningly devised fables", of the Jews on religious questions (1 Timothy 1:4; 4:7; 2Tim 4:4; Titus 1:14; 2Pet 1:16). In such passages the word means anything false and unreal. But the word is used as almost equivalent to parable. Thus we have (1) the fable of Jotham, in which the trees are spoken of as choosing a king (Judges 9:8-15); and (2) that of the cedars of Lebanon and the thistle as Jehoash's answer to Amaziah (2 Kings 14:9).

Source: Easton's Bible Dictionary
Fable

A fable is a narrative in which being irrational, and sometimes inanimate, are, for the purpose of moral instruction, feigned to act and speak with human interests and passions. --Encyc. Brit. The fable differs from the parable in that -- The parable always relates what actually takes place, and is true to fact, which the fable is not; and The parable teaches the higher heavenly and spiritual truths, but the fable only earthly moralities. Of the fable, as distinguished from the parable [PARABLE], we have but two examples in the Bible: That of the trees choosing their king, addressed by Jotham to the men of Shechem, (Judges 9:8-15) That of the cedar of Lebanon and the thistle, as the answer of Jehoash to the challenge of Amaziah. (2 Kings 14:9) The fables of false teachers claiming to belong to the Christian Church, alluded to by writers of the New Testament, (1 Timothy 1:4; 4:7; Titus 1:14; 2 Peter 1:16) do not appear to have had the character of fables, properly so called.

Source: Smith's Bible Dictionary