Quality metrics (PMBOK, pg. 287) are an output of Plan Quality Management. It's those metrics we intend to capture to make sure our product incorporates the correct level of quality. Think about a cheap product you bought recently and think how quickly it was worthless. It was made cheaply because they were massed produced without including the cost of quality (an important concept). There is a trade-off between a higher quality product and the cost of initial product OR the cost to replace the product. Quality metrics are often not something the customer would ultimately be interested in (though sometimes they overlap) - think a new car warranty - free repairs before 50,000 miles. So, car manufacturers build-in quality to at least go PAST the initial warranty. How do they do this? Quality metrics. We plan to watch for certain metrics as we build something. For example, iphones might be weighed as they go down the production line. So, one of our quality metrics would be an upper and lower quality limit on weight and we'd define that in our plan.
Quality control measurements, on the other hand, are simply that, they are the ACTUAL control measurements - lets say we capture the actual weight of every iphone that goes down the assembly line. We take these measurements and put them in the format required by our quality management plan. Maybe this is a dashboard. Maybe iphones are trending heavier in the last month. Are we using more glue? Are we adding unnecessary parts? We would need to investigate. The actual customer requirement (or what Apple has advertised) is that iPhones weigh a certain amount. By planning to control quality and by actually gathering measurements according to our plan, we can verify (important) that we are controlling quality.
Hope this helps.