well, The case is, after leaving central Asia, Juan Juans, as later they'll becomse Avars, crossed through modern Iran and Caucasus, so they might have get mixed with some Iranian Nomadic tribes, and if we consider that some north Caucasian and some nomads in northern Black sea area were Iranic language speaking, and Avaras might get mixed with them as well, then we can actually come to that conclusion.
In fact even before being Avars, Juan Juans themselves were not pure Hunnic or Turkish, they were actually mix of all the nations who run away from China, India and Mongolia. Gumilyov tells that who were criminal or who ever did not like his mom and dad would run to the desert and join to the militias of Juan juan-so called group opf people which later were defeated by GokTurks and leave Central Asia. This is also stated in Rene Groussets - Empires of Steppe.
Coming to white Huns, I believe in early stage, and in later stage as a ruling clan, we can consider them being Huns, however they were in thelands of modern Pakistan and India, so their later military and even economy were consisted of local Rajas and their servants, rather than mobile nomadic horsemen like Huns. If we look late White Hunnic history we can see that they fought with Gok Turks as well, which means they were not 100% same with their northern neighbours. Thats my conclusion, I mean it might be wrong or smth.
thanks