If we look at the prophecies concerning Israel and Christ.
The pre mill people believe Israel will be restored. and the prophesies Christ has not fulfilled yet will be fulfilled at his second coming
the Amil people believe God is done with Israel. The church has replaced Israel concerning the promises. And Christ is reigning and ruling with a rod of Iron today. and has been since he left.
To me it is an interpretation issue..
The Premil people are divided between historic Premil and Dispensationalists. Historic Premil believe that Israel = Jews and Gentiles in Christ through faith in Christ and Israel is being saved every time a Jew or Gentile turns to faith in Christ. Historic premil = post tribulation. Dispensationlist = Pre-tribulation rapture. And number of other differences.
Amil = return of Christ = the burning up of the current earth and universe and the arrival of a new heavens and new earth. No thousand years. Amil = the thousand years has been happening since Calvary. It's a symbolic number.
Postmil = the gospel will eventually rule the world and the church will gradually become more and more triumphant and make the planet ready for the return of Christ.
Preterists = Jesus already returned in 70 A.D spiritually and the new heavens and new earth and thousand years and everything else is now.
Partial Preterists = as above but Jesus never returned in AD70 and is still coming back.
That's the gist of it. Historic Premils don't agree with one another on everything. Nor do Disps. And Amils have the greatest variety of differing beliefs under the umbrella of Amil than all.