Scott started as an ethnic byname: "the Scot," someone from Scotland or marked as Scottish in English and Border records. Clan Scott rose among the Riding clans of the Anglo-Scottish border; the surname also appears early in England for people linked to Scottish lords or identity.
It is not an occupation and not "son of Scott" in the medieval mainstream. Among the product's four types, ethnic bynames sit with nicknames. Irish Scott appears later as a surname borrowing of the same idea.