Testamental-Discontinuity
The new covenant is materially different from the old, not merely differently administered — a dispensationalist tendency rejected by the Standards.
This is a contested or rejected alternative.
The Westminster baseline on Testamental Continuity is One-Substance-Different-Administrations. Personas and schools listed below hold this alternative position instead — either because they argued for it at the Assembly (like the Erastians on polity) or because they represent a receiving tradition that departed from the Standards on this point.
Other positions on Testamental Continuity
One-Substance-Different-Administrations WCF
The covenant of grace is one and the same in substance through both testaments, differently administered (WCF VII.6) — the bedrock of the Standards' use of OT material.
Replacement-Of-Israel
The church wholly replaces ethnic Israel with no remaining peculiar covenantal relation — the Standards leave open a future of ethnic Israel (cf. LC's silence).