Not really. VoLTE is Voice over LTE[1], which most likely implements HD voice (wideband audio[2],) however, with carrier and device support HD voice could be done over 3G and 2G networks as well.

[1] https://en.wikipedia.org/wiki/Voice_over_LTE

[2] https://en.wikipedia.org/wiki/Wideband_audio

VoLTE is great -- I use it on Verizon. But at least with Verizon it is turned off by default and most people don't seem to turn it on. It is turned off by default because LTE coverage is not as complete as the legacy 3G coverage (yet).

Facebook audio as others have pointed out is great.

T-Mobile had it from 2013 and earlier (they got the iPhone5 in 2013 and it supported HD Voice). Call quality can be like a clear Skype.