I am very interested in this too, the TFTNA took a much more direct approach on Max Strength than TFTUA both in naming as a category and in gym based programming. My understanding based on reading both books:
Max strength is largely a neurological stimulus to increase recruitment of motor units. It can be trained via gym and sport specific methods. Gym methods focus on ~4 movements that are most sport specific pulled from general strength routines. 4-6 reps with weight at 80% 1 rep max, 4-6 sets, enough rest between sets to fully recover. TFTNA is very clear on these. TFTUA I believe merges the gym based transition (addressing defficienies), general strength and max strength (to simplify?) into Chapter 7 where the max strength show up as the ‘stage 3’ workouts.
I believe as you note on page 266, max strength is referring to the z5 sport specific methods :early phase of short duration max effort hill sprints (~8-10 sec). As these hill sprint progressions move up in time (and slightly lower in max effort/speed) the effect becomes more metabolic (zone 4). Also shorter duration hill bounding.
This represents getting gym based ‘stage 3’ MaxS into the transition phase, with sport specific maxS in the early base. Based on my life, seasons and training plan I tend to pull more gym based MaxS into the early base for ski touring and extend the general strength ‘phase 2’ through the whole transition.
My only minor criticism of TFTUA is this exact topic, I appreciated the TFTNA differentiation of general strength, max strength and muscular endurance categories. TFTUA however added more nuance and options for the ME as well as the hill bounding/moose hoofing etc options. I love having both books.