In simple terms, strength is about increasing force production. Size, on the other hand, is about getting a pump and creating microscopic damage to the muscle, which then causes it to repair and grow larger. This is hypertrophy in a nutshell.
The general rule of thumb when training for strength is that the reps should be low and the resistance load should be high. Also, true low-rep strength work is primarily neuromuscular. If you think of your body as a computer, strength training is more about upgrading your software, which is your central nervous system (CNS), than it is about the hardware—your muscles. Strength training is about teaching your CNS how to bring more muscle into the game; or to increase motor unit recruitment.