This is all cleared up in the new book: supplemental work is done after the main lift and usually done with a big barbell movement. It can be the same movement as the main lift OR be something similar. It is always a barbell movement.
So squat, dead, press, bench press, incline, floor press, deficit pulls, front squat.
Assistance is dips, rows, core work, single leg work and all that boring stuff. This is not tracked other than with "total reps" per three categories (push, pull, single leg/core).
Just about every program has assistance. Not every program has supplemental.
All facets are controlled per template: main lift, supplemental, jumps/throws, assistance and conditioning work. It's like a recipe and every template will be different. Same ingredients just different amounts. This is called "balance" and a new principle added to the other four 5/3/1 principles.
I PROMISE everyone that this will be explained in the new book in a horribly simple manner and it will be easy to apply to everyone and every circumstance.