Self, soul, spirit, atma
We can understand the soul in the body in several ways. If we have a loving relationship with someone and that person dies, the body is still there, perhaps lying on the bed, yet we fully understand that something—the thing we loved—isn't there anymore. We want the body to go away, and at the same time we miss the person we loved. So obviously the body and the person (soul) are different.
The body is also constantly changing. Once you were a baby. Your body was small, it grew into the body of a child, and now you're older. When you see pictures of your baby body it's difficult to recognize that it was you—especially in comparison with your present body. At the same time you know that you're the same person that was in all those different bodies. Again, it's obvious that the body and the person inside the body (soul) are different.
We're the soul. We live within any given body for some period of time, yet we tend to think we are this body. We spend so much time, money and energy trying to make the body happy. We act as if the happiness of the body would give us the satisfaction we're always anxious for. Unfortunately, this never works.
Because we're the soul, we're never really satisfied unless we're offering the soul the opportunity to be happy. The soul doesn't find its happiness in contact with matter. So if we keep seeking happiness in contact with matter we'll always feel disappointed. The soul requires connection with Krishna, the supreme Soul, in order to find true satisfaction. Until we—the soul—engage in spiritual activity, and seek our happiness in the spiritual realm, we won't be satisfied.