Hi Stephen,
A simple way to look at it would be:
Manage Something = To Do Something
Controlling Something = Monitor Something
For instance, in Project Integration Management, you have "Direct and Manage Project Work" and then you have "Monitor and Control Project Work".
Direct and Manage Project Work
After you’re done planning, it’s time to do the work. Your job is to make sure that everybody is doing what they should be doing, and that the products or services your project creates meet the needs of the stakeholders. Here’s where the work gets done. It’s where all of the planning you’ll do in all of the other knowledge areas comes together so that you can actually make stuff. It’s the day-to-day work that you help your team do, and make sure gets done.
Monitor and Control Project Work
A good project manager is constantly monitoring every single thing that goes on in the project. Remember, the later you find a problem, the harder and more expensive it usually is to fix. Keep everyone satisfied by catching problems as early as possible.
Hope this helps.