it's really not that complicated !! how much does the motor help you, as a function of how hard you pedal... and what's the MOST it will ever help you.
as far as i know every decent torque-sensor system from the big manufacturers works the same :
in the mission control days, specialized called the "how much help do you get as a percentage of your power" parameter "support". top slider of left image. the "what's the most support you get, no matter how hard you hammer it," was "peak power"
for TQ, middle image, "assist" is the same concept as support, and max is the same as peak. for mahle, Pp is "peak power" and "Re" is the same as specialized's support and TQ's assist.
the only meaningful differences are :
1 whether they include an acceleration parameter - specialized does not for road/gravel/hybrid bikes, the others do. that's how quickly the motor ramps from no/low assist to high.
2 whether assist is a direct percentage of your pedaling power, as in the TQ example where it's 200% of your power, no other multipliers or factors. in order to keep the scale from 0 to 100 on all their bikes, specialized added the support factor, which is hidden, and ranges from 1.8 or 2.0 to 3.x plus depending on the bike. that's where the confusion comes in, because people set it to 100% thinking if they put in 100w, the motor also puts in 100w, when in fact it puts in 200w or 360w or whatever.
this is totally just a software thing, they could change it if they felt like it... and keep in mind the SL system was co-designed by specialized and mahle, the full power ones by specialized and brose, so really there isn't anything new here that specialized has done other than what they call the terms and set the scales.