Actually throttle pressure linkage is the correct name. Kickdown linkage is just what alot of people call it just like many guys call an engine a motor which is technically incorrect but we still know what it means. It does perform the kickdown process but it is accomplished by varrying the throttle pressure against the governor pressure.
To answer the question I believe the difference in the 2 and 4 barrell linkage is the height and position it places the cable. I have the 2 barrell linkage on my car and just had to bend it a little to make it work with the 4 barrell setup.