My understanding was tailscale is to connect different machines across the internet, but that a traditional VPN hides your information

You got it! When you google VPN services, you get all these companies selling products for encrypting your internet traffic (90% snake oil IMHO). Main usecase nowadays seems to be making your browsing appear like you are in a different country. This is not what people are referring to in this thread by “VPN”, even though it is the exact same underlying technology.

Tailscale is actually trying to simplify the original VPN idea, which is to create a secure private “network” over the internet, so your devices can securely talk to one another, no matter where they are physically (over the internet). When you are out on the road, your phone can see your home server just like they were on the same home network, and there’s no way for an attacker to see the traffic or get access to those machines. You might also read about Wireguard or Zerotier -same idea, the first is more rudimentary but is used by Tailscale, the second is their main compeditor. Tailscale is pretty good at being easy to get going because it takes care of authentication, routing, and port forwarding for you. They even helpfully proxy your encrypted traffic if the machines fully cannot p2p we each other (slow, but can save your butt). The apps are pretty decent too. I used Tailscale for a long time then eventually self-hosted it once I knew what I was doing sufficiently. I still use their apps.