I'm not sure I fully understand the distinction but I guess the big difference is that very few Christian countries are theocracies (i.e. in these countries Christian religious law has no impact outside the very limited authority held by clergy, e.g. denying entry to places of worship).

But historically as an outside it seems that Islamic sects are fairly analogous to Christian ones. There was an early split between Rome (Catholicism) and Constantinople (Eastern Orthodoxy), later various reformers led to Protestant sects, some of which eventually joined in alliances like the Evangelical Church in Germany (which includes Lutherans and Calvinists but has established a shared consensus).

At a glance, Christianity is defined by a split between Catholicism and Protestantism, with Protestantism being a fairly diverse collection of various groups ranging from Lutherans to Baptists.

Much of Christianity's present form is owed to the Peace of Westphalia, which in a nutshell led to the widely accepted ideology that it's okay for other countries not to share your religious beliefs (or even allow a diversity of beliefs in their own territories).

Thanks for expanding in that. I wasn't aware of Peace of Westphalia.

For what it's worth, early Islam is basically game of thrones. Worth checking out what happened in the decades following the death of Muhammad SAW.

The modern conception of sovereign states that people seem to think is some ancient invariant is actually the result of the Peace of Westphalia and the Congress of Vienna. The post colonial borders were shaped by that understanding.

Do people who grew up in former Ottoman territory have the same conception? Within that empire the idea of nation was quite different.

I hadn't seen that abbreviation before, but it's apparently this: https://en.m.wikipedia.org/wiki/Peace_be_upon_him

Christianity does not have schools of jurisprudences. However in the past the Catholic Church has had opinions on how to govern and in the future "dominionist" sects of protestantism may gain influence [0].

[0] https://en.wikipedia.org/wiki/New_Apostolic_Reformation

In Germany both the Catholic church and the Evangelical church are registered religious organisations governing various religious communities and institutions. The German Catholic church is obviously subject to the Vatican, but the Evangelical church is a lot more democratic, consisting of a large number of otherwise independent religious communities (including Lutherans, Calvinists and Unionists).

This sounds similar though a lot more aggressively expansionist.