You can build a lot of muscle mass without huge gains in strength. Conversely you can build a lot of strength without large gains in muscle mass. Having said that, strength and muscle mass are not mutually exclusive. Obviously in the first case, you will have strength gains (try building 16″ pipes lifting 10 lb weights). In the process of building huge muscle, strength is gained as a by-product. In the second case, the muscle has to grow, which is the by-product of increasing strength.
Let’s explore further, bodybuilding requires more total volume training which means heavy weights at higher reps. The rep range is typically from 8-12 and this makes for lighter weights (due to the higher reps) than strength training. This causes quite a lot of damage to the muscle. In the process of repairing the damage, the muscle grows (hypertrophy). So here, the focus is on growth with strength as a by-product so to speak. Bodybuilders tend to also focus on symmetry and aesthetics…looking for the right proportions.
Strength training is about using more muscle fibers or increasing the motor unit recruitment, which occurs at lower reps (1-5), using heavier weights than bodybuilding. Here the focus is on strength gains with building muscle mass as the by-product. Strength training generally makes use of compound exercises such as deadlifts, bench press, barbell rows, squats etc., working multiple body parts. This develops overall strength. This is not to say bodybuilders do not employ the same exercises. But, in addition to those exercises, bodybuilders also make use of isolation exercises to selectively work a particular muscle (Think leg extension, calf raises, concentration curls…). Bodybuilders also eat massive amounts of calories (proteins and complex carbs) to feed those huge muscle gains. This is not necessarily a big part of a person training for strength. Sure, they are gonna eat the carbs and proteins to help fuel workouts and repair damaged muscle, but not nearly as much as a bodybuilder.
Depending on your goals and inclination you may choose one form of training over the other. I’m not here to judge. Your choice!
P.S. The healthy goat was last seen sneaking into a gym in Harlem. He was subsequently kicked out for head butting a bodybuilder.