Another way in which a taxonomy of Calvinism has been proposed is with respect to the logical (not temporal) order of decrees. The following chart may help, in which in addition to the two Calvinist positions, I've also included the Arminian and classical Amyraldian positions:
|Permission of Fall||Permission of Fall||Permission of Fall||Election of Some to Glory|
|Death of Christ||Death of Christ||Election of Some to Mercy||Permission of Fall|
|Universal Prevenient Grace||Election of Some to Moral Ability||Death of Christ||Death of Christ|
|Predestination of Those who Make Good use of Grace||Holy Spirit to Work Moral Ability in Elect||Holy Spirit to Save the Elect||Holy Spirit to Save the Elect|
|Sanctification of the Predestined||Sanctification of the Elect||Sanctification of the Elect||Sanctification of the Elect|
It should be noted that there are Calvinists in both the "Infra" and "Supra" lapsarian camps. The descriptions Infra-Lapsarian and Supra-Lapsarian refer to the relation of the decree of Election to the decree of the fall (the "lapse" in "lapsarian"). Infra-Lapsarians believe that God elected some fallen men to Salvation/Mercy (infra = after), whereas Supra-Lapsarians believe that God elected men first to Glory (supra = before), and then decreed the fall as a means to that end. Of course, both camps are discussing the logical order, not the temporal order. There have been notable reformers in both camps.
Turretin was a notable Infra-Lapsarian. Twisse, on the other hand, was a notable Supra-Lapsarian. The Synod of Dordt seems to have favored the infra view, while the Westminster Assembly seems to have favored the supra view, while neither council addressed the issue as such in so many words (i.e.neither body specifically stated that God first in the logical order decreed the fall, or first in the logical order decreed to bring some men to glory).
It's generally held in Calvinist circles that both views (infra and supra) are within the bounds of orthodoxy, although, of course, both views cannot be correct. Some people wishing to include Amyraldians as Calvinists have proposed a three-fold division of Calvinism, with Supra being "high," Infra being "moderate," and classical Amyraldianism being "low." There are a number of problems with this view, the greatest being that the classical Amyraldian position has a fundamental error with respect to the atonement, namely that it makes the atonement, with respect to the decrees, indefinite. This error is not present in a "lesser degree" in the infra view and likewise is not mirrored by an excessively definite (is such a thing even possible?) view of the atonement in the supra view. In short, the problem can be expressed as their being no single variable that permits scaling across the three groups.
Instead, the attempted justification for the scaling lies in the fact that the decree of election is earliest in the logical order in the supra view, then the infra, then the Amyraldian, and logically latest (among evangelical groups) in the Arminian view. This justification seems rather artificial, but at least is not totally arbitrary. In any event, though it would tend to provide a way of categorizing people that does not rely simply on buzz-words.
It should be noted that there are a number of Calvinists who don't take a particularly emphatic (or explicit) view with respect to the order of decrees. Thus, for example, Dr. White has mentioned that he has a "modified supralapsarian" position, but I haven't seen a detailed explanation of what means by that (link to source) (I should note that the link itself is a good example of Dr. White distinguishing his own position from hyper-Calvinism long before the recent slander-fest on that topic -- see also this further discussion). The reason for such lack of discussion is that this issue, whether the decree to permit the fall precedes or follows the decree of election, is a relatively minor point. It is not something that would require men to divide fellowship, at least that is my position.