It's not emacs, it's GNU Readline (or likely some BSD readline given apple and the GPL) http://cnswww.cns.cwru.edu/php/chet/readline/rltop.html.
The shortcuts also work in every text field in the OS.
The shortcuts also work in every text field in the OS.
Terminal.app passes the key sequences to the application running inside of the terminal. The default shell (bash) uses GNU readline, which has an emacs-mode and a vi-mode (emacs is the default).
Terminal.app does not use any Cocoa text fields, so has nothing to do with the Emacs keybindings inherited from NeXTSTEP.