What makes something 'another religion'?

I've been pondering lately the question of what makes something a different religion. For example, it is generally accepted that Judaism is a different religion to Christianity. Yet both share much of the same history, worship the same God, share many of the same scriptures etc. Likewise Islam is considered a different religion to both Judaism and Christianity despite a lot of overlap too.

On the other hand, there was a group called the Gnostics in the second century. They believed the creation of the world was an error made by a demigod and that Jesus had been sent by a higher god to help rescue some of the pure spiritual souls that had become trapped in matter. Through secret knowledge of the nature of the cosmos, these souls could escape the realm of matter after death. The Gnostics generally rejected the Old Testament, and had their own New Testament books and gospels. Now I would want to say Gnosticism is a different religion to Christianity. It isn't just a "heresy", but it's another religion entirely. Yet generally it is described by historians of doctrine as simply a heresy. I can't quite fathom that.

Really, the question I have been pondering over the last couple of months, is whether Calvinism can really be called Christianity or whether it must be counted as a separate religion. When I pull my nose out of a book about New Testament or pre-Nicene Christianity and wander out onto the internet, I see statements by Calvinists that simply have nothing in common with early Christianity whatsoever. Of course, the same argument could potentially be made whenever Christian doctrine varies, and thus could be used against all heresies throughout history and all Christians today. However, some differences are obviously more profound than others and Calvinism increasingly strikes me as being so antithetical to early Christianity that it is hard to consider it anything other than a different religion.

If we consider the core doctrines of the early Christian faith:

1. Monotheism
2. Christ as Teacher of Righteousness
   
3. Final Judgment by Works
4. Free Will

Catholicism and non-Calvinistic Protestantism vary between endorsing two to four of these doctrines. Yet Calvinism agrees only with the first and is deliberately and implacably opposed to the other three (ie 2. Penal substitutionary atonement, 3. Judgment by faith and grace alone, 4. TULIP). Like the Gnostics, the Calvinist system of salvation bears no relationship whatsoever to the early Christian view. It also adds in a wide variety of additional doctrines (though is no worse than Roman Catholicism in this regard I suppose). Anyway, over the last couple of months as I have reflected on this, I have become convinced that Calvinism cannot be meaningfully classed as Christianity and represents such a complete departure from NT and pre-Nicene Christianity that it should be classified as a separate religion (at least from the point of view of doctrine - the issue of classifying religions is obviously more complex and has to take into account rituals, customs and practices etc as well).