It is the hundred-constable which originated the term constable, and the parish constable acquired it by comparison; where the term headborough or chief pledge is used in contrast to a constable, the term constable is likely to refer specifically to the role of a hundred-constable.
The hundred-constable was responsible for creating the term constable, which the parish constable later adopted by comparison. When "headborough" or "chief pledge" is used in opposition to a constable, "constable" usually refers specifically to the role of a hundred-constable.