I suspect the root of the problem is that over time, "proxy" has become strongly associated with application-layer protocols like HTTP, and after that shift it wasn't obvious what to use for something lower-level that encompassed a wider range of protocols/endpoints/conversations. In principle, "tunnel" would probably have been better (and a legible metaphor to boot), but that's just not how things shook out in practice.
That is, does the ISP have access to the information that's being accessed via the proxy?
It was my understanding that proxies tending to mask where a request came from but does nothing significant with the data between it and the requester.
VPNs are better (as in more ergonomic) in practice, since large sites tend to block access from known hosting providers (looking at YouTube not rendering video when accessed from a Hetzner server).
It could, but it's not a hard requirement. A proxy server is just like any other server, encrypting the data en route is as desired.
A VPN encrypts data as a part of securing tunnels, but it's not a hard requirement there either. As long as two computers can communicate over private IP address ranges on a WAN, it's a VPN. The Private in VPN indicates the scope of the network, not whether any data within is immediately accessible.
See also: "Private" and "Public" IP address ranges.
>does the ISP have access to the information that's being accessed via the proxy?
The ISP providing internet to the proxy server will know what the proxy server requests and receives.
>It was my understanding that proxies tending to mask where a request came from but does nothing significant with the data between it and the requester.
Correct. Again, whether the data a proxy server receives and forwards was encrypted is tangential to the task of forwarding data.
First, system that forwards traffic behind its own IP address is called proxy if it works on application level, and NAT if it works on IP level. So we have socks proxy, but home router with NAT.
Second, VPN is just a fancy name for an overlay network over WAN. Overlay network is overlay network even if it only contains two nodes - your host and a remote router providing internet access.
I do not have direct experience with these VPN services, but i would guess they work on IP level and not on application level. So they are just ISPs providing service through overlay network (VPN) instead of access network or physical network.
Just google "VPN" or "How do I access Pornhub in Alabama?" All of the results refer to "VPNs" as I was using the term.
A Virtual Private Network is a private network such as a Local Area Network created virtually on a Wide Area Network such as the internet. Tailscale, SoftEther, or Hamachi for the old boys are examples of VPN implementations.
A proxy is a server that accepts and forwards traffic from clients through it, lending its IP address to clients as the traffic origin if desired.
A proxy can exist in a private network, but it is not a requirement.