Do terminal TTYs for iOS and macOS exist?
TTYs exist and operate in Mac OS X and macOS just as they do in any other UNIX or UNIX-like operating system. When macOS boots, the TTY that inits to subsequently load the GUI is always console. Subsequent TTYs opened from Terminal.app or other emulators are listed from ttys000 and the digits increment one at a time.

You can open Terminal and check your TTY as in the examples below:

$ tty
/dev/ttys000


Or

$ who
trane    console  Sep  1 05:18 
trane    ttys000  Sep  1 05:19 
trane    ttys001  Sep  1 05:19


Or

$ w
13:04  up 1 day,  7:46, 3 users, load averages: 1.85 2.02 3.87
USER     TTY      FROM              LOGIN@  IDLE WHAT
trane    console  -                Sun05   31:45 -
trane    s000     -                Sun05       - w
trane    s001     -                Sun05       9 -bash


For more information on those commands, see the relevant man pages. For e.g., type man who and quit using q.

It's worth noting that macOS only runs one instance of the Aqua GUI for a particular display device.