Interesting question, and worth a measured response, either here or in Stack Exchange Biblical Hermeneutics Beta. By the way, I assume you are not after a mere list of different schools of thought vis a vis literalism but an explanation of what distinguishes one "faction" of literalists from another faction of literalists.
According to Dr. Bob Thiel, Theophilus of Antioch, who wrote c. 180 A.D., was one of the earliest proponents of the "literal" approach to biblical interpretation. Thiel, by the way, is known online as COGwriter.com, and he is a widely published spokesperson for the Continuing Church of God (with which I am in no way affiliated). Thiel contrasts Theophilus's approach with the "allegorical" approach to biblical interpretation espoused by Origin of Alexandria, who borrowed extensively from Clement of Alexandria. These two "schools of thought" or "camps" are in some ways the antithesis of each other.
On the one hand, Theophilus, a literalist, would explain the concept of God's anger in very human terms, albeit not in a sinful sense. Call it righteous indignation or an aspect of the wrath of God, but God's anger is literal, according to Theophilus, and its expression is real.
On the other hand, Origin, an allegorist, would insist the human concept of anger is not worthy of God but must be explained not in anthropomorphic terms but in figurative and allegorical terms. In other words, there needs to be a "deeper" meaning than simple, human anger. The literalist camp would insist that while there may in fact be an occasional deeper meaning in a biblical text, the "default setting" (my term, copyright 2013!) for reading the Bible should be literal, not figurative.
Since the third century in the Common Era, variations of the two camps (not to mention other, competing camps) have come and gone. I would not be surprised if by google-ing various key terms in this regard, one might come up with a scholarly work which traces the evolution--or devolution, as the case may be--of the literal method. In fact, I will do that search myself and edit this answer if I find any sources worth quoting.
Additionally, I would not be surprised, either, if someone has written a tome on the various ways in which Christian literalists have gone about the art of interpretation since the first century A.D. Come to think of it, the "higher critics," so called, may in fact be literalists in some ways. What sets them apart from other literalists, however, is their tendency to explain away or discount such things as miracles and even the inspiration of the Scripture by the Holy Spirit. In other words, they may believe there was an actual Moses, for example, but not that Moses spoke to a rock and out gushed water.
The same reasoning applies to the crossing of the Red Sea. Higher critics lean toward believing the sea was a Sea of Reeds, and that there was nothing particularly miraculous in the way the Israelites crossed that shallow body of water that could not be explained through natural phenomena.
I hope someone takes up the challenge I've issued and answers the OP's question based on knowledge which has already be acquired in this regard before I've had time to prepare a more thorough answer than my partial answer.