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