Hale is the northern English and Scottish form of whole, and the pair is a small lesson in how English spelling records dialects. Both come from Old English hal, "healthy, sound, uninjured, entire." In the north the vowel stayed and the word remained hale; in the south it rounded and became whole — which then acquired an entirely unhistorical w in the 1400s that no one has ever pronounced.
So of the two, hale has the more etymological spelling and whole the more corrupt one, despite whole being the standard word. The root means "whole, uninjured, of good omen," and it also gives health, heal and — through the Germanic sense of wholeness as blessedness — holy. It survives mainly in the phrase hale and hearty, and acquired a literary sense of vigorous old age in 1734.
hale (adj.) "in good health, robust," Old English hal "healthy, sound, safe; entire; uninjured; genuine, straightforward," from Proto-Germanic *hailaz (source also of Old Frisian hel "complete, full; firm" (of ground), Old High German heil , Old Norse heill "hale, sound," Gothic hails "hale" ) , from PIE *kailo- "whole, uninjured, of good omen" (see health ). The Scottish and northern English form of whole and with a more etymological spelling. It later acquired a literary sense of "free from infirmity" (1734), especially in reference to the aged. Related: Haleness . hale (v.) c. 1200, "drag, pull," in Middle English used of arrows, bowstrings, reins, swords, anchors, etc., from Old French haler "to pull, haul, tow, tug" (12c.), from Frankish *halon or Old Dutch halen or some other Germanic source, from Proto-Germanic *halon "to call," from PIE root *kele- (2) "to shout." Figurative sense of "to draw (someone) from one condition to another" is late 14c. Related: Haled ; haling . also from c. 1200