Yes, we call them network connections. Everything you do on the Internet uses them.
Aside from the
AF_UNIX socket you are referring to, there are
AF_INET sockets and
AF_INET6 sockets, which make IPv4 and IPv6 connections, respectively. There are a few other types, but you probably don't care about ancient things like AppleTalk...
Unlike Unix sockets, network sockets do not have corresponding files on the filesystem. They can only be created in application code using the socket API (see the socket(7) man page).
In the case of the tuning scripts, they should have command line options that allow you to specify the remote host to connect to. The popular mysqltuner.pl script, for instance, accepts
--port to specify a remote host. (Though specifying the port isn't necessary unless you moved it from the default of 3306).
You still need a username and password with
USAGE privileges on the MySQL server, and the firewall must permit you access.