The second and third parts of a vert kick are the rotation and kick. This is somewhat obvious, but it should be remembered that the takeoff method is a part of this. As mentioned, swing and cheat takeoffs account for approximately 180 degrees of the total rotation in a trick, but pop takeoffs have no on-ground rotation and are measured from the point of takeoff. Simply put, vert kicks begin where the takeoff method initiates, and end where the kick reaches its target. The technique for the kick itself in a vert kick is identical to its grounded counter part, although being airborne can alter the balance points until refined.
The simple rule of thumb is that frontside vert kicks require full rotations to create round kicking tricks, and an extra half to create hook kicking tricks. From backside, this is reversed.
It should be noted that this is where TKT and Mainstream terminology differ. In mainstream terminology, all hook tricks are named with full rotations (360 720 1080), while round tricks are on the halfs (540 900 1260), regardless of stance or the actual rotation of the trick. TKT simply calls tricks by their actual rotations and kick type, but never by stance. For example, both a pop-720 and Backside-720 (implied pop takeoff) are hook kicking tricks. In TKT, these tricks are known by their takeoff type, rotation, and kick type: Pop-540-Hook (Pop-720), and Pop-360-Hook (Backside-720).
The video above demonstrates the rotational progression of hook tricks utilizing the swing takeoff. The caption uses the TKT names, with their mainstream counterparts in parenthesis. Note that the swing takeoff accounts for 180* of the rotation, so the in-air rotation is ~180* smaller than the number indicates.