Obadiah Sedgewick (one of the Westminster divines) shows how there is an internal (absolute) and external (conditional) side to the Covenant of Grace. The former is what is graciously effected in the elect. The latter is what those within the visible Church are brought into. This is preached and offered in the Word and Sacraments.
Of the Covenant in special.
I shall now descend to something more special, to show unto you, what that Covenant which God makes between himself and his people.
There are those who distinguish of a twofold Covenant.
1. There is Foedus absolutum, which is such a promise of God, as takes in no stipulation or condition at all, that runs altogether upon absolute terms; such a Covenant was that which God made with Noah, that he would never down the world any more. Gen 9.11. and such a kind of Covenant is that, when God promises to give faith and perseverance unto his elect, Heb. 8.10, &c. Both these Covenants are absolute, and without any condition; there is nothing in them but what is folded up in the promises themselves.
2. Foedus Hypotheticum, which is a gracious promise on God’s part, with an obligation to duty; for although it be natural to God, to recompense any good, as it is to punish any evil; And although man does owe unto God whatsoever God covenants with him for; yet it so pleases his Divine Will thus to deal with us, that in binding of us to duty unto himself, he binds himself in reward unto us, and promises such and such a recompence, upon the condition of such and such a performance.
Obadiah Sedgwick, The Bowels of Tender Mercy Sealed in the Everlasting Covenant (Printed by Edmund Mottershed, for Adoniram Byfield, and are to be sold by Joseph Cranford, at the Sign of the Castle and Lyon in St. Pauls Church-yard, 1661), 6.