God is very systematic and has put various systems in place throughout time to accomplish His will. This is why math works the way it does and gravity is considered a universal constant. And while math rules and gravity always seem to have exceptions in a specific set of circumstances, God is constant. He never changes.
We see this divine characteristic in the Bible. He is the same yesterday, today and forever (Heb. 13:8). The consistency of God also means that insofar as He has given us insight, we can see how He chooses to relate to us as His special creation, distinct from the animals.
Two major sets of theology exist to put into words the way God has revealed His relationship with humans: Covenant Theology and Dispensationalism.
Covenant Theology has been around for hundreds of years and is at the heart of Reformation theology. Dispensationalism is much newer to the scene, though it has become more commonplace in American evangelicalism in the last 150 years.
Covenant Theology is a way to interpret the Bible that highlights the importance of the covenants for understanding the way God relates to humankind and redemptive history.
Dispensationalism is a system of biblical interpretation that recognizes God-administered “ages” to order the affairs of the world.
Where we all agree
Both CT and DP would not stand if it weren’t for the rigorous belief that the Bible is the infallible, inerrant word of God. This is a massive point of important agreement. The second is on the gospel itself.
This means that any disagreements the two camps might have are simply disagreements within the family. This ought to control the vigor and subdue any prideful tendencies we might have toward those with whom we disagree.
Where we disagree
Covenant Theology teaches that God interacts with man by means of covenants — agreements He sets up, upholds and holds us accountable to. The overarching covenant of redemption is the covenant God has made within the triune godhead. This is the basis for all other covenants involving man. The covenant of redemption is the promise that God is saving His people from their sins — that He will save sinners and bring them to Himself. Anyone who believes in Jesus as Lord and Savior is a result of God upholding this covenant, specifically from God the Father to God the Son with the power of God the Holy Spirit.
Under this is the covenant of works given to Adam by God in Genesis 1–3: how Adam, representing all of humanity, was to obey God. This covenant of works had the consequence of death should Adam not abide by it. As we read in Genesis 3, Adam did not obey God’s commandment. As an everlasting and sequential covenant, the covenant of grace follows from there. In Genesis 3, we see the promise of the seed, pointing to Jesus Who fulfills all the promises of God. And all the smaller covenants of Noah, Abraham and David fall under the covenant of grace.
The new covenant in Jesus also comes from the covenant of grace, where we experience forgiveness of sins in Jesus. While we look back to Him, the Old Testament covenants were looking forward to Jesus. All of Scripture is viewed, then, through this understanding — Jesus came and upheld the covenant of works, was the culmination of the covenant of grace, so He might fulfill the covenant of redemption.
This view tends to see continuity between the covenants of the Old and New testaments and sees the church as the new Israel.
God and humankind
Dispensationalism teaches that God relates to humankind in different ages He has organized and ordained as part of His plan. It understands the Bible to include seven dispensations: innocence (Gen. 1:1–3:7), conscience (Gen. 3:8–8:22), human government (Gen. 9:1–11:32), promise (Gen. 12:1–Ex. 19:25), law (Ex. 20:1–Acts 2:4), grace (Acts 2:4–Rev. 20:3) and the millennial Kingdom (Rev. 20:4–6).
There is a very literal interpretation to most of the Bible in this theology. For instance, when Revelation speaks of a 1,000-year reign, a dispensationalist would view that as a literal 1,000 years.
There also is a distinction between Israel and the Church. According to this view, the Church does not replace Israel, which has distinct promises from old for the ethnic people.
Applications of biblical texts will differ as a result of where you stand. Be convinced, and point others to Jesus. Making much of Jesus should always be the primary point of our theology, otherwise it will be more “me-ology” than theology.
For more resources to go in-depth:
Covenant Theology: https://www.thegospelcoalition.org/essay/covenant-theology/