When the term ~/.gnus.el is used it just means your Gnus configuration file. You might as well call it ~/.gnus or specify another name.
In Gnus terminology a back end is a virtual server, a layer between core Gnus and the real NNTP-, POP3-, IMAP- or whatever-server which offers Gnus a standardized interface to functions like "get message", "get Headers" etc.
When the term Emacs is used in this FAQ, it means GNU Emacs.
In this FAQ message means either a mail or a posting to a Usenet Newsgroup or to some other fancy back end, no matter of which kind it is.
MUA is an acronym for Mail User Agent, it’s the program you use to read and write e-mails.
NUA is an acronym for News User Agent, it’s the program you use to read and write Usenet news.