A settlement agreement and a contract are synonymous.  So the question is really, is there a contract to settle the case?  What are the elements of contract?  Offer, yep.  I will dismiss my case if you dismiss yours and pay me the money we agreed you owe me.  Acceptance?  Yep.  I agree to dismiss and to pay you the amount we agreed on.  Consideration?  Yep.  Both cases are dismissed and they agree to pay the money.  Is the settlement agreement enforceable like any other contract?  Yes indeed.  It certainly is.  And you will really anger the judge if you have to sue to enforce a settlement agreement.