Perhaps we use the same word to describe them because initially they did use the same technologies, but they have branched out ever since? Maybe IPSec would be a common tech used. But the algorithms are not the same anymore since they serve different purposes (Personal privacy vs corporate/sysadmin security)
In the corporate world VPNs were usually a lower level abstraction security mechanism or a redundant security mechanism to either complement application layer_security, or to hot-patch modern security unto legacy LAN systems. VPN encryption is usually provided by the local router. Common algorithms are IPSec/IKev2.
In the personal privacy world, we are talking about a proxy that hides identification such as IP addresses, and pools connections to provide privacy. The actual encryption is not the main security mechanism even, as it only covers the transit between consumer to proxy, leaving (a potentially longer transit) between the proxy to the actual destination.
In terms of purpose and architecture it's closer to bitcoin tumblers, or Tor or Freenet, or money laundering placement. The fact that they call it VPNs seems to me more of a marketing scheme or political play to avoid association with all of the above, than an actual technical or academical description. If someone were to analyse these technologies, I'm sure a neutral or critical approach would avoid uncritically calling them VPNs in the same way that research is published not about Viagra, but on Sildenafil.
That's where my head was at. When i hear my colleagues talk about a VPN, i'm thinking about an IPSEC tunnel and an afternoon of swearing at ios on some outdated ASA. When I hear regular people talking about a VPN, my mind immediately goes to "oh, so you want to watch rick and morty on netflix and don't know anybody hosting a jellyfin/plex server".
When do we coin a new term? Or do we? Does "vpn" turn into a word like "truck" where it's only the context that tells you if we're talking about a 2 axle pickup truck in a home depot parking lot or something pulling a 40ft container unit?
"Crypto" in the 90s meant secret keys and message encryption, nowadays it's the term for the numerous ponzi scheme "investments"...
I don't just mean being able to access some private web interface you have on a private server in your at home, I mean connecting a satellite office to the main corporate office.
But for all of these consumer marketed VPNs, I think your list has 90%+ covered...