SYSTEM is an special account reserved for running services only (as well as "local service" and "network service"), users cannot normally log on into those accounts.
"NT AUTHORITY" has nothing to do with domains, but instead is a special denomination for all built-in system special accounts, like system, and built in groups like users.
There IS a way of actually running arbitrary processes as SYSTEM, but it's difficult and sort of a hack to make it work. The trick is to create a system service that runs a cmd prompt, as system, and from that prompt you become system. BTW, system is even more powerful than the administrators group, so I would use it with care and think twice before opening such things