The Free On-line Dictionary of Computing (30 December 2018):

Message Transfer Agent
Mail Transfer Agent
Mail Transport Agent
Message Transport Agent

    (MTA, Mail Transfer Agent) Any program responsible
   for delivering e-mail messages.  Upon receiving a message
   from a Mail User Agent or another MTA, often by SMTP over
   the Internet, it stores it temporarily locally and analyses
   the recipients and delivers it to any local addressees and/or
   forwards it to other remote MTAs (routing) for delivery to
   remote recipients.  In either case it may edit and/or add to
   the message headers.

   The most widely used MTA for Unix is sendmail, which
   communicates using SMTP.

   [Other OSes?]

   RFC 2821 (SMTP) expands MTA as "Mail Transfer Agent" though
   this is less common.  Alternatives with "Transport" are also
   seen but less correct.

   (2007-06-01)