One example would be for building muscles. Any form of resistance training can build muscles, the only question is to what extent and for what end purpose. Beginners wouldn't usually ask too many questions, assuming that there isn't much variance in training methods, and that you usually can't go wrong with the trainer's advice. I won't go into the intentions of the trainers, as some may be altruistic in nature and actually care for your well being, while some are just useless meatbags that spew inane drivel and empty promises in their attempt to swindle hapless old you. There aren't really any wrong training styles (with the exception of wrong lifting techniques), but there is a significantly different end result with each of these styles.
For instance, power training is a method which typically emphasizes short, intense workouts with short rest periods and with exercises that improves strength and athleticism. This training style is usually performed by athletes which want to increase their strength without sacrificing flexibility or mobility. Other benefits would include increased muscle size, and of course improvement of health. In the end, the trainee's initial goals are met, with the additional advantage of increased muscular power, strength, and athleticism.
On the other hand, some gym goers would go with a workout plan that involve heavy weights, high training volumes, and exercise movements that don't go the usual full range of motion. This usually would yield greater muscle growth than the power training described above, but the trainee's flexibility and mobility would be jeapordized if he continuously trains without going for the proper range of motion for each exercise. He'll look bigger, but his body would eventually be stiff as a log.
As you can see, both training styles yielded muscle growth, but to different extents and with a significantly different end result. So in the end, it really depends on what you really want to gain from training. Yes, you'll build muscles and lose fat. But ask yourself another question, do you want to be a stiff musclebound freak? Or a Flexible, semi-musclebound freak who can run, jump and move like an athlete. Think about it.