The serial port remains a serial port - it makes no difference what software is using it for what purpose.

Again, a DCE is a modem; anything else is a DTE - including a "computer" and a "terminal"

The classic use of modems - from which the terminology arises - is the remote connection of a terminal to a computer via modems and a comms network:

           RS232            Telephone Network             RS232
Terminal <=======> Modem1 <--------------------> Modem2 <=======> Computer
  DTE               DCE                           DCE               DTE

Although DTE = Data Terminal Equipment, the "Terminal" in this context simply means that it is at the "end" of the link - not that it is a piece of equipment called "A Terminal"