If somebody was going somewhere and I grabbed their shoulder and stopped their progress, I would say "I caught her by the shoulder." If the shoulder of my shirt is hooked or stopped by something (very seldom a person), I would say that my shoulder is caught. "The hook caught my shoulder and ripped my shirt." Also, if something hit me on the shoulder, I would use that phrase. "The bullet caught his shoulder." Notice that if something hooked onto my shoulder or tangled it, I could use either phrase.

Not sure of your question but he caught her shoulder doesn't make any sense. This means she threw her shoulder up into the air and he caught it! To catch somebody by the shoulder means you grab their shoulder.