Wilson means "Will's son." Medieval Will was the everyday short form of William and of other names built on the Germanic element wil ("will, desire"). Once hereditary surnames stuck, Wilson marked descent from a man called Will—not a specific famous William for every family.
British and Irish lines share the same pattern; some Scottish and northern English clusters are especially dense. It sits squarely in the parent's-name bucket with Johnson or Jackson. Folk stories that invent a single Wilson clan founder for all bearers overreach.