“I didn't catch that. Did you hear what he said?”
You're watching a movie with your friend and you didn't understand something that a character said. You ask your friend this, hoping he can clear up the confusion.
I didn't catch that. Did you hear what he said?
This means to hear and understand what someone says. It's mostly used in questions or negative sentences:
Did you catch what she was saying?
I couldn't catch his meaning. What was he trying to say?
A clause is often used after "hear" to explain what news or information someone has heard:
Did you hear what she did when she found out about the wedding?
I heard that they're going to tear down the old school and build a new one.
I couldn't hear what they were talking about.