It can be a confusing question: what's the difference between muscle building and strength training? Let's break it down so you can uncover the specific goals you'd like to achieve.
Building muscle, or making muscles grow larger, is a physiological process. It involves the tearing down of muscle tissue in order for them to repair and grow. This sounds like a brutal process, but this is actually what your muscles must do, like your biceps, before they can get bigger. Skeletal muscle is probably the most adaptable tissue in the body. These are the muscles that are attached directly to your bones by the tendons. When you take on an exercise, like lifting a weight that is quite heavy, this causes structural damage to the muscle cells. However, this doesn't result in permanent damage. The human body is pretty remarkable; it is in a constant state of healing, even when under stress. After the damage has been done to the muscles, they go into an automatic state of repair. And not only that, as the cells repair themselves, they also multiply. This essentially can make the muscles grow larger. Now, this would probably only happen if the same muscle fibers endure repetitive damage.
Let's say that you would like to have more toned and shapely bicep muscles. Performing bicep curls at the gym on a regular basis, for example, may create that result. At first, lifting the weight may be difficult to do. The muscle fibers undergo damage (you may even experience some soreness), but the cells in the muscles repair and replicate. They are preparing themselves for another assault or further damage, so they get bigger. As stated, when this is a regular process, the muscles accommodate by growing bigger so they can take on the next bout of heavy (or heavier) weight.
Now, this is different from building strength. Having bigger muscles doesn't necessarily mean you are stronger, although the two are correlated. Let's take a look.
Strength is the amount of power needed to exert yourself physically to perform a task. Strength is measured by how well you can withstand pressure. This can also be related to mental challenges as well as physical challenges. Referring back to your growing biceps, lifting the heavy weight does require some level of strength. As mentioned, at your first attempt, the weight may feel very heavy. Lifting it only once could be quite hard; you have not yet developed what is fully required to endure the pressure. But, over time, as your muscles grow AND you're consistent at lifting that weight, you train the muscle to lift it with ease. Further, as you grow stronger and the muscles get bigger, you'll thereby be able to lift heavier weight.
These explanations of muscle building and muscle strength can be attributed to just about any exercise. Whether you're wanting bigger and stronger arms, back, or calves, the concept is the same. Just start out slowly, begin with light weights and shorter repetitions, and be consistent. Over time, you'll see and feel the changes in your body.