The word “to lead” has its roots in the Old English word lædan, meaning “to cause to go with oneself; march at the head of, go before as a guide, accompany and show the way; carry on; sprout forth, bring forth; pass (one's life).”
The word “to manage” has its roots in the Old French word manège meaning “to handle, train, or direct” a horse, “the handling or training of a horse; horsemanship.”