(a) When the claimant proceeds under this chapter for availing himself or herself of that claimant's lien and institutes any personal action for the same demand or any part thereof or for a demand of which the amount for which the claimant claims a lien is a part, it shall be no objection in either suit that some of the parties defendant in the 1 suit are not also parties defendant in the other suit. In any such personal action or in the suit to avail himself or herself of the lien, whichever is last docketed, the plaintiff shall file an affidavit setting out the demand in each of the suits and stating to what extent the respective demands are identical. The judgment in either of the actions shall not be pleaded as a bar in the other action.
(b) Whenever any moneys are applied on the judgment on either of the demands pursuant to the execution thereof or pursuant to any other execution proceedings, the Superior Court may order all or any part to be credited on the judgment in the other of the demands according to the equity of the matter as the equity appears to the Court.