Where did you find that definition of intensity?
Wouldn’t we all agree that to increase intensity you would need to either do:
(1) More work in same amount of time
(2) Same amount of work in less time
Work = force x distance
So it’s easy to see how to do more work:
(1) Heavier force moved the same distance
(2) Same force moved over a longer distance
In this instance force is the “weight” you’re lifting and distance is the number of “reps” you’re doing.
If you think about it, it’s no more difficult than that.
Both definitions are valid. That was another point that was counter-intuitive that Arthur Jones made. That given a specific training protocol, that if you do it in less time than you did it before then it was more intense. Someone protested that if a workout took 25 minutes but you did it in 20 it was a better more intense workout? Yes, it is, the same amount of work done in less time. Many conflate duration with intensity. Training long with training hard when they are in many ways mutually exclusive.
For our purposes here, not getting into overly scientific or technical jargon or theories, I define intensity for the sake of this discussion as the amount of effort one puts in performing a single set. If you can move a weight for 8 reps and can no longer do a 9th strick rep, then it should be obvious that the initial reps are easy and don't require a huge amount of effort. By the time you barely eke out that 8th rep you have increase intensity of effort much more when compared to the first rep. If you continue with further intensity variables: forced reps, negatives... then momentary intensity is further increased.
This one specific definition. The others: less rest, more work in the same time period, are other intensity variables. Of course, a major factor that is often overlooked and almost impossible to measure is cognitive effort. The will and drive to push yourself to your limit. Many believe that they are pushing themselves but your body is always going to try to convince you've done enough as it wants to avoid pain. You just think to yourself that you pushed that weight as much as you can and just couldn't get that 9th rep no matter what so you conclude that was maximum intensity. But if someone offered you a million dollars or Arthur Jones (as he was reputed to do) having a gun to your head, to get that one more rep you might suddenly find that there was indeed a little bit more left in you. That's where competition, a training partner, or a coach can play a role. Pushing you to a level you would not push yourself.