This process of lifting a heavy weight several times, then immediately doing the same exercise with lower weight for many reps, is called strip or drop sets. (They go by some other names, listed here.) It is primarily a bodybuilding method, since they are geared towards training a muscle group to failure for the purpose of increasing muscle size instead of strength or power. As bodybuilding.com puts it:
Bodybuilders are unique among athletes because they're concerned purely with cosmetic improvements and not athletic performance. That's why bodybuilders prefer drop sets - because they're decidedly geared towards increasing muscle size (hypertrophy). By contrast, you don't see a lot of football players, sprinters or other athletes using drop sets, because drop sets are not conducive to strength, power or speed gains. In fact, most athletes want strength and power without bulk, so drop sets are usually nixed. However, if pure mass is what you're after, then drop sets are ideal!
That said, they certainly can produce strength gain. Nearly any exercise can. If someone is sufficiently unadapted to exercise, something as simple as walking can produce massive strength increases. Does that mean walking is optimal strength training? Maybe for them (or maybe not), but not for most people. It may be effective for a limited time in a portion of the population, but it is not a maximally efficient use of time or energy.
For instance: push-ups are less efficient for increasing strength than gymnastics exercises or bench press, but if someone using just push-ups is dedicated, they can get very big and very strong. That doesn't mean push-ups are best for someone looking for strength and size, but it doesn't mean it won't work. (NB: a sub-optimal strength or hypertrophy program adhered to diligently, is superior to an optimal program executed with poor adherence, or with insufficient rest or nutrition.)
One specific variant of drop sets that might be optimal for you is low-rep drop sets (ibid):
This was a favorite method of Larry Scott, the first Mr. Olympia. Scott used this technique to develop monstrous deltoids and arms, even on a less than genetically optimal frame. Larry believed that heavy weight and low reps (six reps) were the best way to develop size and strength concurrently.
This rep range allows you to use heavier weights, which can help maintain your strength levels and thicken up those muscle fibers without much of a pumping effect. Begin with a six rep max, then drop the weight by about ten to fifteen percent with each drop. Repeat with the lighter weight for six more reps for the desired number of drops.
If your goal is size and strength both, and you like this method (with high reps or low), keep at it. I suspect that your strength increases will taper off fairly quickly, since drop sets rely more on strength-endurance than strength. But even at the point when strength gains decrease, you'll still probably be getting bigger.
One caveat that I would agree with, as I am wary of consistently high-intensity programming for most people (ibid):
Use Drop Sets Sparingly As A High Intensity Method. Drop sets are intense and they require caution and common sense. If you used them all the time, you would quickly burn out and overtrain. One great way to use drop sets is the 3:1 method: you perform three straight sets of an exercise, followed by one drop set.