While all Calvinists believe in unconditional election, many differ on how this is to be understood. The following dichotomies are common among Calvinists:
1) Single/double predestination
2) Conditional/Unconditional reprobation
None of these dichotomies are equivalent to the others, but some necessarily entail others. In the following article, I will try to help to alleviate some of the confusion commonly surrounding these dichotomies and the various relations obtaining between them.
Single predestination - Those who believe in single predestination affirm a decree of election but deny that there is any such decree as that of reprobation. Instead, single predestinarians believe in 'preterition', according to which God passes over those whom He has not elected, justly leaving them in their sins. Single predestinarians thus see a very radical discontinuity between God's decree of election and reprobation.
Double predestination - Those who believe in double predestination accept a doctrine of reprobation. Among double predestinarians are:
a) Infralapsarians - The elect and reprobate are foreordained to their respective destinies with a view to the Fall. God contemplated man as fallen in Adam, saving the elect unconditionally, and foreordaining the reprobate to condemnation on the basis of their sins. Hard infralapsarians believe that God chose to "ordain" the Fall prior to His decision to elect some and reprobate others, whereas soft infralapsarians argue that God "permitted" the Fall prior to His decision to elect some and reprobate others.
b) Supralapsarians - High supralapsarians believe that the elect and reprobate are foreordained to their respective identities without a view to the Fall, "after which" God decided to create humanity. Low supralapsarians switch the two. God "first" decreed to create humanity, and "then" chose whom to elect and whom to reprobate. In either case, predestination of the elect and reprobate to their respective identities does not entail having contemplated them as fallen in Adam. Rather, God's decrees of election and reprobation are totally antecedent to any consideration, not only of the merits of the elect, but of the demerits of the reprobate.
A third group, teleological supralapsarians, emphasize God's purpose, end or intention in His decrees. What makes this variant of supralapsarianism unique is that all of God's decrees involving the salvation of the elect, as well as His decision to condemn the reprobate, are antecedent to His decrees to ordain the Fall and create humanity. Thus, God first decreed to save the elect, and then decreed to apply salvific benefits to them through the Holy Spirit. Finally, He decreed to provide salvation to them through Christ.
Infralapsarians and supralapsarians both affirm double predestination. Both of these kinds of double predestinarians agree with single predestinarians that there is a degree of discontinuity between God's decrees of election and reprobation. The asymmetry consists in the fact that while both agree that God monergistically intervenes in the lives of the elect in order to work faith and righteousness in their lives, He does not actively intervene in the lives of the reprobate to cause them to commit evil. He does indeed foreordain their rebellion and condemnation, but He does not work in their persons in precisely the same manner as He does in the elect. They thus both avoid the false teaching of equal ultimacy, according to which God monergistically works unrighteousness in the reprobate in the exact same manner that He does work righteousness in the elect.
Conditional reprobation - This is the view of reprobation taken by infralapsarians. The elect are graciously chosen out of the fallen Adamic race, with the reprobate being justly passed over for their sins.
Unconditional reprobation - this is the view of reprobation taken by supralapsarians. The reprobate are foreordained to condemnation not on the basis of an antecedent consideration of their moral state in Adam, but purely on the basis of God's righteous decree.
I do not believe that Sproul's definition of reprobation as a kind of "divine permission" accurately describes the nature of supralapsarianism. Supralapsarians, and even some infralapsarians (particularly "hard" infralapsarians) affirm that God did indeed positively ordain the Fall, as Sam Storms points out. There is therefore a sense in which supralapsarians do conceive of reprobation as being more symmetrical with reprobation than infralapsarians do. Like infralapsarians, however, we do not believe that God monergistically intervenes in the lives of unbelievers to make them wicked. They are already wicked. Equal ultimacy thus provides an unbiblical anthropology relative to God's decree of reprobation.
One of the key differences between supralapsarians and infralapsarians has to do with differing conceptions of divine justice relative to reprobation. For infralapsarians, God's 'justice" consists in punitive justice, by which God justly leaves the reprobate in their sins and punishes them accordingly. For supralapsarians, the righteousness of God in reprobation consists first and foremost in His personal righteousness, according to which He is "just" in all His decrees, including His decision to ordain the Fall, and to predestination the wicked to condemnation.
Since infralapsarianism conceives of God's righteousness in reprobation as punitive, it follows that infralapsarianism necessarily entails conditional reprobation. It also entails a degree of passivity in reprobation, since God merely abstains from extending His effectual grace to the reprobate. While supralapsarians agree that God is just in condemning the reprobate for their sin, we also hold that God is righteous even in ordaining the reprobate to this very sin, and that this predestination to sin and condemnation is antecedent to consideration of their demerit in Adam. This is where the active/passive and positive/negative distinctions come into play. We deny that God monergistically works unrighteousness in the reprobate in the exact same manner that He works righteousness in the elect. In this, supralapsarians and infralapsarians are in agreement. We differ from infralapsarians, however, in conceiving of reprobation as bare permission. We see it as a positive decree rather than merely in a negative abstinence which consists in bare refusal to extend effectual grace to the reprobate. One could interchangeably use the dichotomies "active/passive" or "positive/negative" with respect to either God's anthropological activity relative to the wicked activity of the reprobate, or God's decree of that selfsame wickedness. But the important conceptual distinction to keep in mind is that, although we see God's decree of reprobation as positive (or active), we deny that this is the case with respect to God's activity in the reprobate anthropologically.
Here is a brief list of Sam Storms' distinctions between different lapsarian views:
a) Hard infralapsarianism
b) Soft infralapsarianism
The only difference between hard and soft infralapsarianism involves disagreement concerning whether God permits or ordains the Fall.
a) High supralapsarianism
b) Low supralapsarianism
c) Teleological supralapsarianism
The only significant disagreement between high and low supralapsarianism involves whether God's decree to create humanity is antecedent to His decree to elect and reprobate. Teleological supralapsarianism departs from both in affirming that all of God's activity in saving the elect and decreeing reprobation is antecedent to His decisions to create humanity and ordain the Fall.
Distinctions between various -lapsarian theories - http://www.samstorms.com/all-articles/post/divine-decrees
Sproul on single vs. double predestination - http://www.the-highway.com/DoublePredestination_Sproul.html