One of the key differences between amillennialism and postmillennialism is how they relate the economy of redemption to the economy of consummation. To put it differently, amillenialism and postmillenialism disagree on the relationship between the Great Commission and the cultural/creation mandate. This seems more or less to be the crux of the issue, at least at the dogmatic level (not necessarily at the exegetical level).
The issue works as follows. In Scripture, there are two basic projects: creation and reconciliation, or consummation and redepmtion. The project of creation is the original setup. You could say “Plan A,” ignoring for now the fact that God always knew and planned for everything else. In creation/consummation, God creates the world and humanity good but incomplete. They are both designed to bring Him glory and receive His grace, but man as God’s image is tasked with bringing this end to its fullness. Man is to take the raw goodness of God’s creation and fashion it into something greater and more beautiful, taking the world from glory to glory. This is what has been called the cultural mandate.
Of course, man’s fulfillment of the cultural mandate was almost immediately upset by sin. The Fall represented the introduction the intrusion of a foreign element, sin, into creation. Sin is diametrically opposed to God, the darkness to His light, and thus its introduction into humanity and the rest of creation prevents the complete fulfillment of the cultural mandate. While man can still advance the creation toward God’s glory to some extent by industry, art, language, and other products, the ubiquitous taint of sin will obscure the image. There will be dark spots, stains, and structural weaknesses at nearly every point. If the cultural mandate is to be fulfilled, sin and death must be removed from the world. This is the project of redemption. The work of Christ is the means by which sin is removed, restoring man to his proper status and role as God’s image.
The division between millennial views emerges here, at the intersection of creation and redemption. If redemption solves the problem of sin which interrupted the project of creation and consummation, then when does the creation project get back on track? The world still needs to go through the process for which it was intended: being brought by humanity from glory to glory in order to display the glory of God in as much fullness as creation can. When and how will this take place?
Amillennialism and postmillenialism answer this question differently. In amillennialism, the project of consummation cannot truly get back underway until the project of redemption is complete. As long as sin and death still exist, mankind will not really be able to fulfill the cultural mandate. Until humans are fully redeemed, the unredeemed elements of human culture will so poison the project as to make its effects null. Only once Christ returns and completes our redemption will we be able to move on and fully glorify creation as intended.
Postmillennialism offers a different answer. In postmillennialism, the projects of creation and redemption operate in parallel. As God redeems, He enables and calls forth the fulfillment of the cultural mandate. This means that the cultural accomplishments of redeemed man are not going to be perfect, since redemption is not yet perfected, but this can be improving in an ongoing way, and in the end purified when Christ returns. So in the time between the first and second advents, we are able to make real progress on both the Great Commission and the cultural mandate simultaneously. The atonement has not only brought redemption to the world, but in bringing redemption has put the work of consummation back in business.
This difference is basically why theonomists and Christian Reconstructionists are nearly all postmillennial. Their project assumes a degree of temporal unity between the two great projects. Work on creation and work on redemption can overlap and interlock. By contrast, this is why so many Reformed Baptists become amillennial but few become postmillennial. Baptist ecclesiology and anthropology tend to assume that the economy of consummation is entirely separate from the economy of redemption, and thus that the cultural mandate is mostly impossible to implement on a scale of any consequence before the Great Commission is finished and Christ returns.