Yes, the origin of
TTY in Unix is from teletypewriter. The tele in telephone, teletypewriter, etc comes from a Greek root meaning far or distant.
phon (sound) = Speaking at a distance and so on.
Timeshare systems (pre-Unix) developed physical terminals that allowed you to interact with (share) the computer during your scheduled time. These terminals meant you did not have to be physically in front of the computer to use it. You could also send output to a teletypewriter, that would print the output at that location.
This was the existing physical infrastructure when Unix was developed, so it was natural to use it for Unix networking. Emulation in virtual or software terminals of the features in physical terminals prevented older code or network infrastructure from breaking.
It's this origin in physical terminals (and ultimately the machines origins in the telgraph (distant writing) system and their use of control codes that accounts for certain terminal standards today. These include the standard 80 character width and the carriage return and linefeed codes.
telein telephone, teletypewriter, etc comes from a Greek root meaning far or distant. TTY's provide a virtual interface similar to what the physical machines provided. This is the origin of the 80 char width and the carriage return and linefeed codes.