The IF-1000 is a Tascam unit, it is mentioned in the MTS-1000's manual. actually the manual is for both units. Parallel and serial are mentioned in all the Tascam manuals, I dont know the significance of either.
Parallel- a separate wire going from master to slave for each command. One wire for stop,one wire for play etc.
Serial- a single pair of wires that sends data packets from the master to the slave, which decodes them to tell the slave what to do. Like your computer keyboard
The ES-50/51 has no way to directly control the MSR/TSR serially,though there is a connector on the back of both the ES-50 and the MSR/TSR for parallel control-transport functions only.