Working set — what counts as work
A set at your working weight, hard enough to build strength and muscle — usually with no more than 3–4 reps in reserve.
A working set is one you do for the result, not to get ready. Working sets are what people count when they say "10–20 sets per muscle a week", and they're what the diary logs. A set after which you could have done 8 more reps is closer to a warm-up, even if the program calls the weight a working one.
A working set's effort is easiest to describe with RIR or RPE: RIR 1–3 is enough to grow. "3×8" means three working sets of eight; the warm-up comes separately.
The diary counts working sets per muscle group for the week and shows where you're in range and where you're under.
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In the diary I work out all of these numbers myself — you just log the set.