Okay, I just opened a 120 back and the insert has the winding mechanism, the counter and the gear that fits through a slot and mates with a gear in the camera body. The back has a pair of leaf springs but it is to hold the insert tight while the insert has the pressur plate springs. The back itself is an empty shell with no mechanisms whatsoever. So, a 120 or a 220 insert will fit and work. Hope it answers the question. The 35mm back is different and neither the 120 nor the 220 insert will fit.
By way of logic, think of the ETRS-C body with the fixed back. It will take either the 120 or 220 insert so the counter, etc. must be part of the insert or it would not work with both.
For what it is worth, I prefer loading a few backs and carrying them than playing with inserts while out. Much easier and faster to swap, especially with the 1 tab early back, and less chance of light intrusion.