WiFi calling uses Internet data (can't think of a better term, sorry) to make phone calls . It's a protocol that is different from traditional cell tower/Volte phone calls in which you need to have a provider and plan to make calls. WiFi calling is free as long as you WiFi to use (unless you're one of those plans that can charge you per minute of use even for WiFi calling).
WiFi calling is the alternative to tower phone calls in the sense that if you don't have a good cell signal, turn on WiFi and you're all set (uses Internet to transmit the packets of data in which your voice has been turned into to transmit to the other phone) . Phone uses less battery than if it were trying to make a call using the tower because it's not tying as hard to stay connected, since the connection point to the router is closer to the tower at that point.
Volte uses 4g speeds to make clearer more crisp phone calls, but I honestly can't tell the difference between a 3g and 4g call (so maybe I'm not the best reference).
Though when I used WiFi calling for my g4, it sounded better than my Volte. On my g4 And i now I use Hangouts Dialer (no WiFi calling for my international model, that I know of) it also sounds better than when I used Volte for my g4.
Though Hangouts dialer is a Voip set up.
Here are references
Since LTE is a data-only technology, LTE network operators could handle voice via “fallback” techniques, making use of the still-existing circuit-switched networks. However, some LTE networks offer “carrier grade” digitized voice directly. Conceptually it is Voice-over-IP (VoIP) on LTE, but there is a lot more to it than that. VoLTE vs. VoIP: What’s The Difference?
Typically, over-the-top VoIP applications like Skype and Google Voice rely on the Internet to deliver packets. The problem is that Internet delivery is done on a “best effort” basis; all you can do is get your packets to the cloud and cross your fingers. VoLTE, on the other hand, uses the IP Multimedia Subsystem (IMS) and new radio access network features to ensure low latency, improved error correction in fringe areas, and other features that guarantee voice service as good as or better than any we’ve ever experienced.
If all the technology works as planned, even those of us who remember telephones with rotary dials will be amazed at the quality of the calls we’ll be making in the not-too-distant future, as well as the innovative new services that will be bundled with VoLTE.
Source:
https://www.spirent.com/Blogs/Wireless/2015/June/2012-09-25_VoLTE_vs_VoIP_Whats_the_Difference