Listening by Webster definition is to hear something with thoughtful attention : give consideration
Monitoring by Webster definition a device for observing a biological condition or function
As you can see one requires you to action while the other just has you looking and doing nothing. When working with social media you must be able to both of these really well. You must be able to observe any kind a trends that are happening and then decided if you are going to react to them or not. Listening it company feedback is important in the fact that the way you handle it can make or break you.
In short: Monitoring finds symptoms; listening finds causes.
If you find the cause then you can help your bottom line.