This one confused me as well when I was studying for the PMP exam.
Just remember this single sentence: Manage Quality focuses on defect prevention, while quality control focuses on defect identification.
*Manage quality is synonymous with quality assurance.
Here's more...
Quality assurance guarantees that the plan was efficient to avoid any anticipated defects. Quality control helps you find defects in the deliverable and correct them.
Quality assurance is a proactive process which starts even before the work on the deliverable has started, while quality control is a reactive process and its activity starts as soon as you start working on the deliverable.
Quality assurance is a process-based approach; here you develop the process to create the product, while quality control is a product-based approach where you make sure the product is as per requirements.
Quality assurance involves processes managing quality, and quality control is used to verify the quality of the product.
A quality audit is an example of quality assurance while inspection and testing are examples of the quality control process.