Here’s what the historic Reformers and scholastics mean by the law/gospel distinction, starting way back with Olevian and Ursinus in the 16th century. The law/gospel distinction is not an OT/NT distinction, for the law/gospel distinction is found in both testaments; furthermore, the OT/NT relationship is in a different category than the law/gospel distinction.
“There is not the same opposition throughout between the Old and New Testaments as there is between the law and the gospel. The opposition of the law and the gospel (insofar as they are taken properly and strictly for the covenant of works and of grace and are considered in their absolute being) is contrary. They are opposed as the letter killing and the Spirit quickening; as Hagar gendering to bondage and Sarah gendering to freedom, although the law more broadly taken and in its relative being is subordinated to the gospel.”
“But the opposition of the Old and New Testaments broadly viewed is relative, inasmuch as the Old contained the shadows of things to come (Heb. 10.1) and the New the very image (ten eikona).”
That’s a dense yet excellent paragraph. I don’t have time to unpack it all, but notice the covenant of works/grace distinction, which is tied into the law/gospel distinction. Usually these all stand or fall together. Also, notice Turretin’s excellent and careful use of words, especially “contrary” and “relative;” those are worth reading over a few times. If I can summarize, Turretin says the law/gospel “opposition is…contrary,” while the OT/NT “opposition…is relative.” That is simply brilliant!
Francis Turretin, Institutes, XX.XXII.VIII.xv (easier: pages 236-237 of volume two); very closely related is Turretin’s discussion of the Mosaic covenant on page 264 (and around there).