Some guy in the gym finishes a hard set of barbell squats and re-racks the weight. He feels realy tired and he takes a big swig from his water bottle. He looks down at his watch and presses the start button to begin counting down backwards from 2 minutes.
He read that 2 minutes is the ideal rest time between sets in the gym, and he wants to get it exact. Once that watch beeps at the 2 minute mark, he'll be back in the squat rack to perform another set. He stands up tall and paces around trying to catch his breath in preparation for his next battle with the weights.
2 minutes is up. His legs still feel weak, his heart still beats frantically and he doesn't quite feel 100%, but that watch beeped and that means his time is up. He must perform his next set regardless of how he feels.
So, he starts the next set. His legs are burning and he wishes that he could have had more time to prepare for this set. He starts the set, but just with a mediocre effort. He finishes the set. Again, he push the button. He does'nt know but, just as a lot of guys in another gyms, he is making a big mistake.
Working out in this way is really far from efficiency. His effort level is far less than his maximum potential. If he doesn't change the way he trains, he will sacrifice a great ammount of muscle growth.
Muscles grow because of an adaptive response to stress. You lift X amount of weight for Y number of reps, and your body adapts to this level of stress. In order to see continual gains in muscle size, you must continually force X and Y to higher and higher levels.
It's quite simple: it's about lifting as much weight for the greatest number of reps that you possibly can. And repeat, and repeat, and repeat...
Because of this, you must always go into every single set of every single workout at your maximum strength potential. By sacrificing the amount of weight you can lift, you sacrifice the amount of muscle you can build. And there is no worse way to make this sacrifice than by not providing your body with enough rest between sets.
You should only begin your next set when you feel that you can perform it with 100% of your strength potential. A stopwatch cannot tell you when that time has arrived; only you can by listening to your body and relying on your own instincts.
A deadlift and a tricep pressdown aren't exactly in the same boat here. After a heavy set of deadlifts to failure I'll usually be resting for at least 5 minutes, often even more. A set of tricep pressdowns is obviously not as taxing and may only require a rest period of 2.5 minutes for me to feel fully recovered.