It looks like web deploy is just a different way of calling msdeploy. I've read some documentation but still don't understand the difference between the two.
It's still referred to as the "Web Deploy tool" but I don't understand what distinguishes it from msdeploy.exe.
Microsoft Web Deploy is the official name, while msdeploy is the name of the executable.
You can download and install Web Deploy from a place such as Microsoft Downloads,
https://www.iis.net/downloads/microsoft/web-deploy
And then you can use msdeploy command, as it is installed to
"C:\Program Files\IIS\Microsoft Web Deploy V3\msdeploy.exe"
So in a simple way, the two are the same thing.