"barrel or cask for soap or liquor; iron vessel," according to Century Dictionary ranging from 72 to 120 gallons, c. 1400, from Old French ponchon, ponson "wine vessel" (13c.), of unknown origin.
Formally identical with puncheon (n.2) "pointed tool for punching or piercing," "but connexion of sense has not been found" [OED] and the best guess at it seems to be from the stamp or imprint impressed on the barrel via a puncheon. Uncertain connection with another puncheon "short slab of timber, strut, vertical wooden beam used as a support in building" (mid-14c., from Old French ponson, ponchon), which Middle English Compendium regards as identical. Punch (n.2) in the drink sense is too late to be the source of the "cask" sense.
"pointed tool for punching or piercing" used by masons, also "die for coining or seal-making," late 14c., from Old French ponchon, poinchon "pointed tool, piercing weapon," from Vulgar Latin *punctionem (nominative *punctio) "pointed tool," from past-participle stem of Latin pungere "to prick, pierce, sting" (from suffixed form of PIE root *peuk- "to prick"). Punch (n.1) is a shortened form of it. The meaning "stamp, die" is from c. 1500, a specialized use.