catch (something that a person 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?

hear (dependent clause)

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.