Strength and power athletes train to predominately increase what's called myofibrillar hypertrophy, and bodybuilders train to predominately increase sarcoplasmic hypertrophy
To understand what's going on, you first need to know the anatomy of muscle tissue.To prevent this from turning into human biology 101, there's just two important things you need to know:
This is where contractions happen and is the core of the muscle (far left on diagram above). When a muscle contracts, two filaments inside the myofibril, called actin and myosin, slide along each other to shorten the muscle. When the muscle relaxes, the actin slides back again to lengthen the muscle.
This is the next layer outside of the myofibril that contains a fluid like mix around the myofibril called sarcoplasm. This is where immediate nutrients and energy units are stored to fuel myofibril (muscle) contractions; like a petrol tank to your car's engine. This includes glycogen (chains of stored glucose), mitochondra (the powerhouses for energy - click here to read more about them), calcium ions, and myogloblins (oxygen supply).
The Two Types of Hypertrophy
This is what performance athletes such as olympic weightlifters, powerlifters and strength athletes are chasing - actual increase in size and strength of the myofibrils (the filaments that contract and shorten the muscle). This occurs from performing heavy, low rep work of roughly 80-90% one rep max (1RM) for 2-6 reps and increases strength and power substantially, like increasing your car's engine size and power output. The only problem is this is a very slow and subtle process. These filaments do not greatly increase muscle volume (the size of the entire muscle), which is why someone can be as strong as an Ox, but appear not much bigger than an average person.
This what your bodybuilders, fitness models, physique and endurance athletes are chasing - large increases in muscle volume (size). This, funnily enough, doesn't actually increase muscle strength by much, if any! Instead it increases muscular endurance by increasing the amount of sarcoplasm surrounding the myofibrils, like increasing the size of your car's fuel tank! This occurs from using lighter weight for higher reps; roughly 50-75% 1RM for 8-20 reps. This is due to the fact that when training in this weight/rep range, your muscles actually fatigue from running low on nutrients to sufficiently fuel muscular contractions and from too many waste products building up inside the cells. It's not that your muscles aren't strong enough to continue, it's that your fuel tank is empty and your engine can't get rid of all the fumes being generated! When you rest between sets, your muscles have the opportunity to refuel and remove metabolic waste products. Your body is very good at improving this issue, and can easily increase sarcolemma size to store a greater amount of sarcoplasm, and thus more nutrients and energy units for the myofibrals to continue contracting, therefore leading to a fast and large increase in muscle size and volume - providing your diet is adequate to allow this growth to occur of course.
So while it's important to train in as many areas as possible to develop a good foundation and improve strength, power, speed and muscular volume, it's extremely beneficial to know what is the most appropriate training protocol for your goals. If you want to build muscular size and endurance, train in the higher rep, lower weight range. If you want to build strength and power, train in the lower rep, higher weight range. However, don't let it become your only training protocol; you can only get so strong, or increase sarcoplasm volume so much, until you have to start other training protocols to allow your body to break plateaus and continue to progress in your main goals. Training in only one or the other style will also cause your physique to lack certain qualities, such as either being too 'soft and round', or lacking good shape. Balance is key and every style of training has its benefits that can assist you in continuously progressing.