Wrap is arguably not an actual transition, but is a misidentified swingthrough, and is not even mentioned in the Aeriform system. Because it is so deeply ingrained in the tricking collective consciousness it has been included.
Some people argue that wrap is a swing into a sideflip, which only fuels the argument that it is actually a misnomer. Aside from the various uses of the word by some members of the community to describe a cheat takeoff from backside, or an over rotated cheat takeoff, wrap is a swingthrough type transition in most cases.
Thrown from backside, or inside stances, wraps are somewhat similar to both front swings and master swings in some ways. The wrap generally takes off somewhere between the two, but can potentially be confused with either, depending on how the technique is performed.
In vert kicking, wraps tend to mimic a swingthrough or frontswinging motion tinto a cheat kick, as a transition, although quite often what is labeled and understood as a wrapthrough into a vert kick is performed more like a rapid or missleg. This ambiguity somewhat confuses exactly what a wrap is, or isn’t. Despite these varying uses, the wrap term is widely utilized and accepted within the community.
It should also be noted that the wrap transition, if it is one, is the only transition that can only be done in one way. While there are multiple types of every transition, each utilizing either leg, depending on the situation, the wrap is really only done from relative backside or inside stances, and only with the inside leg as the base leg.