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).