There seems to be a predominant view among orthodox Presbyterian theologians today regarding membership in the covenant of grace that posits a distinction along the following lines: there are elect and regenerate true believers who partake of the "substance" of the covenant, whereas unbelievers who are members of the church only partake of the "administration" of the covenant, sometimes even further qualified as the "merely external" administrative realities of the covenant. This is an attempt, on the one hand, to account for the rich biblical data regarding the real privileges of covenant membership in the Church, the real possibility of apostasy of covenant members, and the sovereignty of God in the salvation of all the elect. On the other hand, this particular way of formulating the distinction seems to have been hardened in the wake of the Federal Vision controversy in American Presbyterian life over the past decade, as theologians have reacted against the more extreme Federal Vision proponents who fail to make any spiritual distinctions between covenant members who persevere and those who don't.
Unfortunately, a distinction along the lines of "substance" vs. "administration" or "internal/spiritual" vs. "external/formal" quickly runs into serious problems and rightly faces charges of latent Platonism, dualism, and mere sacramental memorialism (sloppily called "Zwinglianism" at times). In order to preserve the proper subjectivity--which needs to be acknowledged!--regarding the varying experiences of church members within the covenant of grace, almost all objectivity whatsoever has been obliterated from the category of covenant. This is misguided, for the following reasons.
1) The Hebraic and biblical worldview never makes such sharp distinctions between internal and external, spirit and material, substance and administration. Paul occasionally uses inner/outer distinctions as in Rom. 2:28-29, but a) his point there is more eschatological ("flesh"/"Spirit" contrast) than ontological; and b) he is speaking about ultimate spiritual realities; he is not saying that Jews who were not "true Jews" of heart were not, after all, true covenant members with every advantage afforded by such membership (as Rom. 3:1 goes on to prove). Actually, Rom. 2:25 proves that the previous covenant membership of a disobedient/unbelieving Jew is not called into question; rather the blessings of circumcision ("praise from God," vs. 29) are forfeited, because the "circumcision" has become "uncircumcision."
2) Because covenant is itself the category by which we account for the historical, conditional sphere of God's condescension to relate dynamically with His people, there is no need for a further category like "administration of the covenant" to account for the reality of people's varying responses to the grace of the gospel offered in the context of the Church. The decrees of God, including the decree of election, is carried out historically by means of the covenant of grace. The "covenant of redemption," or pactum salutis brings into view the full salvation of all, and only, the elect of God. The covenant of grace, by contrast, brings into view, as true and full members of the covenant of grace, all members of the visible Church of God, marked formally by baptism. As history progresses, the various responses and experiences of different people, within the context of this covenant, result in the outworking of God's sovereign decrees of both election and reprobation (the "historical process of differentiation," as Van Til called it).
Covenant is not coterminous with salvation. As paedobaptists, we recognize this most of the time in our language when arguing for the necessarily "mixed" nature of the covenant community even in the new covenant era. However, when we come to this question regarding the members of the covenant of grace and whether that category should be broader than the elect, many people start hedging and creating these new distinctions of types of covenant membership to account for apostates. We need to make some kind of distinction, of course! But Scripture knows nothing about varying levels or degrees of covenant membership. Covenant is the objective, visible, historical realm, in the context of which God carries out His secret counsel in the decree of election.
3) There may be no more powerful way to illustrate and prove the previous point than to consider the dual-sanction nature of the covenant of grace. It is a widely acknowledged biblical principle that from him to whom much is given, much will be required. The more revelation and covenantal advantage received by a person, the more serious the judgment if he or she is unfaithful. What is not fully appreciated about this dynamic by many Presbyterians, however, is the fact that these enhanced judgments on apostates are covenantally qualified, and that by the terms of the covenant of grace of which they were a member!
Consider: the apostate in view in Hebrews 10:26-31 is subject to a much severer judgment than a breaker of the Law of Moses was (v.28)! Therefore, the judgment in view is not simply the base-line eternal judgment for all sinners outside Christ, who are in Adam, and will suffer the consequences of the broken covenant of works; rather, the judgment is qualified by the fact that they were afforded, by their membership in the covenant of grace, every opportunity of knowing and bowing the knee to Christ, even having drawn near to Him in a certain sense, and then deserted Him. This judgment is a negative sanction of the covenant of grace, and it is nothing if not "substantial".
A more specific illustration of this is the Lord's Supper. While Paul's warning in 1 Cor. 11 is primarily directed to true believers, and reminding them that they may undergo the disciplinary judgment of God if they partake in an unworthy manner, the broader principle is this: because the Lord's Supper is a covenant meal, there are powerful spiritual realities that are objectively operative in the Supper. Christ is present. To be sure, Christ is present for blessing and received for salvation only for those who partake in faith. However, it is precisely the objective presence of Christ in the Supper that accounts also for the judgments experienced by those who partake who shouldn't, or who partake selfishly. Compare the horrific reality of the "presence of the Lamb" in the judgment scene of Revelation 14:9-11.
The covenant of grace is the vehicle for sinners to have eternal fellowship with God, but is not itself the category of loving fellowship. Covenant is wider than salvation--at least this covenant. The covenant of redemption is no wider than the circle of the elect who respond to Christ in faith. But we must not confuse these two covenants.
4) Some Presbyterians have appealed to the above "substance" vs. "administration" distinction in order to deal with the quotation of Jeremiah 31 in Hebrews 8, which speaks of the newness of the new covenant in which "all will know the Lord, from the least to the greatest." In order to answer objections from credobaptists who understand the Jeremiah passage to teach that only regenerate people are true members of the new covenant, some paedobaptists will say that they agree in one sense--the sense in which only those who are partakers of the "substance" of the covenant are truly members of the new covenant in the fullest sense, even though there is also this wider category of the "administration" of the covenant.
An obvious objection to this argument is that if this substance/administration distinction has been the case for every era of redemptive history (which these Presbyterians will say is the case), then Hebrews 8 is not successfully explaining anything about the newness of the new covenant. If "all will know the Lord" has been true for the "substance-partakers" in every administration of the covenant of grace throughout history, from Abraham to David to Christ, even though there have been many more "administration-partakers," what's so new about the membership situation in the new covenant? It seems one is automatically forced back to one of the other interpretive options for paedobaptists that does not appeal to the substance/administration view at all: either the prophetic hyperbole/corporate perseverance of the Church view, or the priestly-class-distinction-breakdown view.
Conclusion: God has condescended to carry out His decrees in covenant relationship with human beings. First in a covenant of works with Adam, and then in a covenant of grace with all visible members of His Church throughout the ages. Not all these visible church members were elect, regenerate, or will be eschatologically saved. However, they were all truly in covenant with God. That's the precise reason the apostates are judged more harshly. The distinction we need to make has to do with the responses of various covenant members--yes, responses of faith are only enabled by the Spirit carrying out the intra-trinitarian plan of the pactum salutis--not the supposed "degree" or genuineness of their covenant membership. Covenant membership is as plain as baptism and church membership; eternal salvation is a narrower category within the covenant of grace, not a parallel covenant.