thats the thing with snaps: they go all over the place on your system, so even if you uninstall it (which itself is a tiring and cumbersome task at times!), they magically stay everywhere on the systems, with tons of folders and files.
They're downloaded somewhere under /var/snap and by default a snap only has access to a limited set of directories - one under /var/snap for system-wide data (generally used by snaps that run services like cups or MySQL) and one under ~/snap for each user. When you snap remove an app, it bundles that up into a file that's kept for a while in case you reinstall, but it won't if you use --purge.
Obviously many apps request access to other places (such as non-hidden directories in your homedir) so they can read or write stuff, but that's down to the app to then behave correctly (same as with any other packaging system).
install yes, but there are tons of other files and folders that get created, IIRC even pseudo-users or something along those lines? (or that was distro-specific perhaps)