Even the Hebrew, " מוּסָֽר׃ " or transliterated "musar" is translated at "disciplines."
The proverbial idea of "spare the rod, spoil the child" is from at least 1377. This can be seen in the writing The vision of William concerning Piers Plowman by William Langland. In it he wrote, "Who-so spareth ye sprynge, spilleth his children." "Spryge" could mean "sprig" which would be like a rod. "Spilleth" at that time meant "spoil." However, it is probably older, as can be seen since the idea is probably from the Bible.
None of these say, "spare the rod, spoil the child," though.
It was Samuel Butler's poem, Hudibras , from 1662 that is the origin of the exact form of the phrase that we use now. It is a satirical poem about factions in the English Civil War. It goes, "Love is a Boy, / by Poets styl'd, / Then Spare the Rod, / and spill the Child."
Spill was a commonly accepted form of the word "spoil" in 1662.
The phrase probably became popular and evolved as the English language evolved.