Why did he use "catch"? Does the meaning become different if he says "see"?
"Catch" in this context has the same meaning as "see". He uses "catch" here because "catch" implies seeing something that you might not have seen (for different reasons). For example, his friend might have not been paying attention to his last "move", so he's asking if his friend "caught" (meaning "saw") it. Ex: Do you want to catch a movie tonight? Ex: I caught fifteen minutes of the concert before I had to leave.