Redemptive-History focuses on the development of doctrine as it is revealed throughout the history of salvation. This is the history of God working to save a people for Himself, to defeat death and break the effects of the Genesis 3 curse, all culminating in the Kingdom of Heaven. The central character as well as the plot are all centered on the person of Christ. As such Redemptive-Historical Theology (or Biblical Theology as some would have it) focuses on development and context in relation to Christ as opposed to logical structure and ordering.
This is not to say that Redemptive-Historical approaches dispense with logic but rather it is subordinated and found within God's unfolding revelation itself. It is therefore of a different (or transcendent) order and this is why (depending on context) it can seemingly change or work in different ways. Think again of Paul's discussion of the Law in Galatians 3. It was temporary and served a purpose but was fulfilled and passed away. Thus it would be erroneous to simply pull verses from the Old Testament Law and apply them to today's context without first reading them through a Christocentric New Testament lens.From God's promise in the Garden that the Seed of the woman would crush the head of the Serpent, to the lives of God's servants who testified to the prophetic, priestly, and kingly offices of the coming Savior, all the images in the Old Testament, whether it be the wars, the Holy Land, or the Temple - all pointed to Christ. He is both Savior and Judge and the central focus of God's creation in both this age and the age to come (Ephesians 1:21, John 5:39, Luke 24:44).
Paul also touches on these issues in Romans when he discusses saving faith and how Abraham (though living under a different covenantal order) was ultimately justified even as we are. Some things stay the same but are given in different forms depending on their context. The Epistle to the Hebrews is rightly described as Redemptive-Historical theology at its finest - and yet it also is probably (aside from Revelation) the most controversial and debated book in the New Testament. For many, its interpretations of the Old Testament and its framing of questions surrounding salvation and assurance are not only at odds with common understandings, but utterly baffling and upsetting. Regardless, it excels at elaborating Old Testament typology, how it has been fulfilled and how the New Covenant is superior and eternal.
The New Testament reveals some fascinating dynamics - akin to the facets of a jewel that change depending on how they're viewed. Sometimes the Old and New Testaments are presented as a continuity - Moses as a kind of prototype prefiguring Christ. Other times, there's strong tension with the Old Testament being described as a ministration of death (2nd Corinthians 3:6-9) - and thus sharply contrasted with the New. Elsewhere (as in Galatians 3) Moses represents a parenthesis, a temporary order, while the true continuity is found in the Abraham-Christ connection. We have the interplay between law and gospel which mean different things at different times. We also see the tensions between grace and works in both Old and New Testaments operating in ways not always easily pinned down - despite what some would say. It always seems to depend on the context and we find this is how both Christ and the apostles taught and revealed doctrine. We find these same tensions when it comes to questions regarding things like assurance and the sacraments - not to mention the doctrine of the Trinity and the Person of Christ.
The result is not ambiguity or subjectivity - a scenario in which nothing can be pinned down, but rather a vibrant theology that focuses on the unfolding of revelation as opposed to the grid-like tendencies of systematics and its heavy reliance on human logic.
For some this very logic is central and they would argue it cannot be separated from the doctrine of God. Others will posit that Paul dismantles human logic and philosophy in the opening chapters of 1st Corinthians, leaving us with a reliance on revealed truths and mysteries - understood by means of the Holy Spirit.