Considering universality for all types of SAS, functionality of each stages and so on, I propose the naming on the digital system below.
Type-A:
F0 - F1 - F2 - F3 - BF - PF - MAR - IM - TM
Type-B:
F0 - F1 - BF - IM - TM
Type-Bp: F1 - BF - IM - TM
(* Recoil-mass chain is omitted because this is a naming of the "stages")
(* Sorry I'm not sure about the Type-C )