What is the difference between between Aqualyx and Kybella? And how come only Kybella is FDA approved?

They work by the same mechanism, as both are forms of the same active ingredient.  Deoxycolic Acid is a molecule that occurs naturally in the body and helps us to breakdown and absorb fat in our diet.  When injected into the fat cell, it causes it to breakdown and be absorbed.  Only Kybella is approved for use in the US.  The approval studies targeted the fat under the chin, so that is the only currently approved use. Although this molecule could theoretically target fat anywhere, using it outside of the submental area is currently "off label" in the US.  The approval process is different in other countries, and the company that distributes Aqualyx describes using it in other areas as well.  But performing the studies to obtain FDA approval is expensive, and has not been done yet in the US.  I would recommend that you see a board certified plastic surgeon to see what may be best in your case.

Kybella (Belkyra in Canada) is the only FDA and Health Canada approved injectable treatment to treat submental fullness (double chin). The only area approved for it's use is the double chin area. Some physicians may be using it off label, however, at our clinic we stick to approved indications. All the best. 

You are correct. Both products are similar. However, only Kybella is FDA approved, but only for fat under the chin. This means that a lot of research has gone it to both it's safety and efficacy. Although surgeons are trying Kybella in other areas of the body, referred to as "off label" use, make sure to see a board certified plastic surgeon in your area with lots of Kybella experience to ensure that it is safe.Kindly,Kouros Azar