Can a Terminal Emulator on android do everything that a terminal on linux or mac does? I downloaded a couple terminal emulators onto my android phone and wanted to know what the limitations on them are. Is there anything that a terminal can do the emulators simply cannot?
Not really.... they are no more limited than the tools that Android has installed, remember that Android is not Linux, it is based on it but it's command line interface is very limited by comparison due to the fact that all the tools needed for a full Linux implementation are not needed with Android. The capabilities can be increased significantly by installing BusyBox though. 

Don't be confused by the term "emulator" all terminals you are comparing it to (like Linux terminals) are all terminal emulators. Technically, a "terminal" is a physical device, like a Wyse 60 or Televideo 955 terminal, which contained no intelligence for processing data, it just displayed the information as a "terminal" to the mainframe. The terminology has stuck, and we use the term "terminal emulator" to mean any piece of software that is used to emulate a physical terminal.