I grew up in a "Baptistic" tradition, so it has been very difficult to get past the presuppositions I didn't even realize I had. It's like a whole 'nother way of thinking, this Covenant Theology thing.

I kinda set up the differences in 3 categories: Different hermeneutic, different covenantal views, and different ways of interpreting the "Regulative Principle of Worship:"

On Hermeneutics:

The Presbyterian hermeneutic is described in the Westminster Confession of Faith this way:

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The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith, and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture… (WCF 1:6, emphasis mine).

The Reformed Baptist hermeneutic sounds similar but it is different because it does not include deduction or “good consequence:”

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The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith and life, is either expressly set down or necessarily contained in the Holy Scripture (London Baptist Confession 1:6, emphasis mine).

So what’s the difference? I have a silly, simplistic way of illustrating it: If one passage explicitly states that “all normal dogs have four legs,” and another explicitly states that “Spot is a normal dog,” then it is necessarily true that Spot has four legs even though that fact is not explicitly stated. The fact is contained in the book even though not explicitly. A Presbyterian might deduce that since there are other properties of normal dogs, such as two ears, a wet nose, and a wagging tail, then Spot must also have those qualities as well, even if the book doesn’t explicitly contain those things in its description of normal dogs. A Baptist could not reach that far, since two ears, a wet nose, and a wagging tail are not explicitly contained in the book’s description. Have I understood this correctly? I have no idea, really, since even the Apostle Paul uses "good and necessary consequence" from the Old Testament scriptures in his epistles to explain his doctrines.

On Covenant Theology:

Presbyterians view the Old and New Testaments as containing different administrations of the same covenant, which most refer to as the Covenant of Grace. They do this to preserve the continuity of Scripture between both Testaments. But to a Baptist, it isn’t necessary to preserve the continuity of the Testaments by describing the two as being “different administrations of one covenant.” The writer of Hebrews describes the Old Covenant as “type and shadow” of the New. The New fulfills the Old. To a Baptist, the two are separate covenants altogether and while one prefigures the other, they apply to different groups of people and different points along the continuum of unfolding eschatology and progressive revelation:

First, the Old covenant was limited, under it’s different administrations, to one family, one race, one nation; whereas the New removes all such distinctions.

Second, the Old was temporal rather than eternal as the New covenant is.

Thirdly the Old was physical, geographical, and political, where the New is spiritual, universal, and “not of this world.”

Yet under the Old Testament, prefiguring the New, all who were eternally saved were saved just as they are in the New: By faith in One who was to come, the Seed promised to Abraham in the Old covenant, the Second Adam, the Mediator of – as the writer of Hebrews describes it – “a better covenant based on better promises (Hebrews 8:6).”

I reject the second premise altogether, since all of the covenants (Abraham, Moses, David) were to be "everlasting, throughout your generations." Also since the plan of salvation is the same between them all, I tend towards the "one single covenant of grace" idea. How 'bout putting it this way: The New Covenant is new in relation to the Covenant of Moses which is the one Jews lived under in Jesus' day and still do in our time.

On the Regulative Principle of Worship:

Both Reformed Baptists and Presbyterians subscribe to this principle, based on Sola Scriptura and described in the Westminster Confession of Faith in these terms:

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…the acceptable way of worshiping the true God is instituted by Himself, and is so limited by His own revealed will, that He may not be worshiped according to … any other way not prescribed in the holy Scripture (WCF 21:1).

This principle has been reduced by many people to simply, “When it comes to the worship of God, whatever is not commanded is forbidden.” This is quite unlike the Lutheran and Anglican principle which is, to reduce it to it’s simplest form, “whatever is not forbidden is permitted in the worship of God.” This leads them to all sorts of human inventions that “help the people worship,” from drama and dance to more superstitious stuff like making the sign of the cross and assigning mystical properties to the elements in the Lord’s Supper. Superstition, by the way, I take to mean trying to please, appease, delight, or “reach” God by any means other than revealed in His written word.

Because the Old Testament is to be interpreted through the lens of the New Testament, and because of the difference in the two views of covenant theology, the Baptist does not see baptism as a New covenant “replacement” of Old covenant circumcision. And as there is no explicit command in the New Testament to baptize any but confessed believers, Baptists reject what Presbyterians call “covenant baptism” (or “infant baptism”). To a Presbyterian, the command to baptize the infant children of believers is “necessarily deduced ” by the examples of Old covenant circumcision and “household baptisms” in the New Testament.

Have I boiled this down properly to it's essentials? I do not wish to misrepresent either side in this debate, so please correct my mistakes and/or false assumptions.