Great question, and I think the # of reps in your example might be well expressed as:
A. 3 sets of push ups to fatigue: X, less than X, less again than X (where X = muscle fatigue, the one set max)
B. 3 sets of push ups to a # that is significant, but not your one set max.
In this case, I think A would require more work than B. Muscle growth is proportional to tension under time, which I think A is more likely to do than B. That's not to say that B would have no effect. Multiple hard sets will make you a lot stronger, for sure.
Lots more depends on what else the person does to support muscle growth: nutrition, sleep, destress come immediately to mind.
BTW, I propose we declare a moratorium on the term "muscle failure". I have seen patients who did pull ups, burpees, thrusters, wall balls, box jumps to "failure," until rhabdomyolysis turned their urine to the color of iced tea. That's muscle "failure" -- the tissue simply cannot handle the physiological stress on it.
I think a better term is "muscle fatigue", meaning you cannot do another rep _with_correct_form_. That is, not only the primary muscles but also the accessory/stabilizing muscles have been worked out.
@Damer , thoughts on this?