An idiom is a short expression whose literal meaning is different than its intended message.
Like a stitch in time saves nine - while literally true of a sewing situation - in used in a more general sense - about nipping problems in the bud early before they get more out of control and require much more effort to fix.
Proverbs are broader biblical stories - old testament - attributed to King Solomon - which are intended to tell a tale but also deliver a message about morality and wisdom in day-to-day living.
Fair to say there is some overlap in intention between idioms and proverbs.
Piece of trivia: Solomon was the son of King David who is attributed with writing the Psalms, which is the chapter that precedes Proverbs.
The word proverbial is often misused in today's society. People will lob in a proverbial in just about any sentiment. Like one might say something like, "Mudcat is being the proverbial smarty-pants."
But there is no actual proverb of the smarty-pants in the christian bible.