What's the difference between supererogate and supererogatory?

Supererogate

Definition:

(v. i.) To do more than duty requires; to perform works of supererogation; to atone (for a dificiency in another) by means of a surplus action or quality.

Example Sentences:

(1) In addition, the results support the proposition that children's concepts of obligation underlie judgments to codify law, that justice reasoning builds on concepts of welfare, and that with increasing age discretionary moral reasoning incorporates such character traits as benevolence, sacrifice, and supererogation.
(2) Supererogatory acts are considered by some to be part of medicine, whereas others accept supererogation to be a gratuitous virtue, to be extolled when present, but not to be demanded.

Definition:

(a.) Performed to an extent not enjoined, or not required, by duty or necessity; as, supererogatory services.

Example Sentences:

(1) These duties follow from four general ethical principles--respect for autonomy, beneficence, non-maleficence, and justice--plus the self-imposed supererogatory duty of medical beneficence.
(2) He argues that an important element of being a health care professional is the assumption of a special and supererogatory obligation to benefit one's patients, even when this entails real risks.
(3) That the afference of the truncal system appears to enter the cord at the last two thoracic segments supports earlier conjectures about a supererogatory static function of the kidneys.
(4) Supererogatory acts are considered by some to be part of medicine, whereas others accept supererogation to be a gratuitous virtue, to be extolled when present, but not to be demanded.