I'd have to see that specific study to know exactly what it said, but here are a couple general things to consider when you're trying to figure out the most effective ways to increase strength. There are two basic factors involved. One is what's called "neuromuscular adaptation," which is about training your existing muscle fibers to operate at their maximum capacity. This involves lots of factors, like increasing the amount of fuel stored in muscle cells, and recruiting more muscle fibers to perform a given activity. Most of the time, our daily activities only activate a relatively small number of the muscle fibers available. So, the first step in increasing strength is to do things that activate more muscle fibers and you can accomplish this by "fatiguing" your muscles in various ways--by lifting a relatively heavy weight a few times, by lifting a lighter weight more times, or simply by doing things you don't normally do, so your muscles get trained to operate in different ways. In this situation, muscle "fatigue" simply means progressively pushing your muscles a little bit further than they routinely go. Basically, your muscles will keep getting better at whatever you make them do, until they get to the point that they can't get stronger without also getting larger. Doing lots of repetitions with relatively low weights tends to increase endurance more than strength, and vice versa, so the best approach during the neuromuscular adaptation phase may involve using both approaches.
When you get to the point that increasing strength requires more muscle mass, "muscle fatigue" starts getting more technical. The second factor involved in increasing strength requires actually increasing the size of your muscle fibers (larger muscles can exert more force)--this is called "muscle hypertrophy." Once you've gotten your muscles to the point that they are producing all the strength they can at their present size, then increasing strength will require adding new muscle mass. To do that, you have to work the muscle hard enough to actually break down the muscle tissue, which typically means using maximum force in a short time (ie, doing sets with low reps and very high weights). Muscle fibers get bigger during the process of recovering from this "breakdown." So, in this situation muscle fatigue literally means getting to the point that you can't do another repetition, and the most efficient way to do that is use higher resistance and lower repetitions.
So, it's not surprising that the study you mentioned could show similar gains in strength using those two different training approaches. It would only be surprising if the people in the study were experienced bodybuilders who were already at the point of maximum neuromuscular adaptation, and their goal was to increase muscle size.
Since most of us don't typically use all our muscles every day in ways that push them to their current limits, it's very possible to achieve significant increases in strength and functional fitness using a wide variety of activities and intensity levels. As I mentioned earlier, your muscles and your cardiovascular system will get better whenever you consistently challenge them to do a little bit more than they are used to doing. That can include improving muscle endurance, increasing the maximum amount of force you can exert one (or a few) times, and using your muscles in different combinations and ways (swimming instead of running, or power yoga instead of weight training, for example).
If your goals include adding new muscle mass to increase muscle strength even further, then at some point you'll need to include the kind of training normally associated with bodybuilding--i.e, the traditional high resistance, low reps, working to total muscle fatigue approach.
Hope this helps.
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