I'm not sure this is true universally. I just spoke to a friend for the first time since I got a phone that does "HD" calling, and although I've been speaking to them for 25 years on the phone, I didn't recognize their voice. I feel like POTS and edge->3g calling made me miss out on a lot of detail and intonation. I'm just glad I get to experience this call quality with non-technically inclined friends before I go completely deaf.
I use a lot of voip services and there's something to be said for the phone companies actually making a competitive product, here.
I suppose one could argue that "HD calling" is technically just VoIP as well.
VoIP systems negotiate codec choice on call initiation, generally using a "best common denominator" rule. Even when only companded PCM is available (PCM-a, PCM-µ), 64kbps will be used since it's the universal norm on the TDM (conventional) telephone newtwork. Unfortunately, as a capacity measure GSM specifies very low bitrates for voice connections, as low as 5kbps in the worst case and 10-20kbps typical. This requires the use of high-efficiency vocoders like CELP variants that are sufficient for intelligible speech but, well, only for that purpose.
"HD voice" is exactly VoIP and with few exceptions is only transported over SIP or a SIP-like protocol using the existing RTP negotiation mechanism, which usually ends up selecting 64kbps companded PCM (same as a landline phone). Increasing use of VoLTE, which is essentially an optimized form of SIP designed to "combine" session control features with LTE for lower overhead, has made this pretty common as HD voice support is standard from VoLTE vendors. There was such a thing as HD Voice over 3G using a similar mechanism that leveraged HSPDA but it was never very common, at least in the US.
VoLTE will quickly become the only way to make cellular phone calls in the US which we can expect to make HD Voice pretty universal. Right now it can be spotty when calling between networks, depending on how their peering is set up.
I use a lot of voip services and there's something to be said for the phone companies actually making a competitive product, here.
I suppose one could argue that "HD calling" is technically just VoIP as well.