There is a big intersection between Aerial Yoga and Yoga Trapeze, if not they are one in the same. A positive take away from this naming confusion is it shows how exciting and relatively new on the scene this style of yoga is and how its full benefits are still being unlocked by those who practice. Hang Out Yoga aims to be at the forefront of these developments and enhance it further still.
You could say Aerial Yoga follows more in the direction of the Iyenger tradition and has a slightly spiritual element as well as being more passive, static and yin whereas Yoga Trapeze is more yang. Although there are Yoga Trapeze teachers out there who are also incorporating that yin element more into their classes and practice.
To further complicate matters there are other activities that use a different type of an inversion sling more similar to a hammock or aerial silk that have started to call themselves Aerial Yoga. However, these activities do not use handles and are better described as falling under the category of AntiGravity Fitness developed by Christopher Harrison which is rooted more in a gymnastics and dance background but has then has been adapted into AntiGravity Yoga.
At least when popularising the name Yoga Trapeze this does not bring any of the associated confusion that can be arrived from calling this practice Aerial Yoga although the two can quite rightly be used almost interchangeably.
The only noted difference between the two is that the "official" Yoga Trapeze sold by YOGABODY Naturals is slightly smaller in size than the yoga sling produced by Gravotonics.