Semantically: those services are acting more like encrypted proxies, with some kind of exit far away from you physically.

VPN's are usually used to create Virtual private networks. Extending your LAN across several sites using software, or granting you access to your LAN when you're not physically located close to it.

It's hard to imagine why the meaning has changed as much as it has, because even though a consequence of this connection can be that you exit to the internet via your destination networks internet connection; I feel like this isn't the original use case at all, similar to how you can use a chair as a ladder.