Critical to Quality (CTQ) - is a parameter, internal to the process which has a direct and significant effect on the outcome of the process. If CTQs are controlled well, it ensures that the product or service will meet customer requirements
Metric - is a standard or a level of measurement. It has two parts - a number followed by a unit. E.g. 72 hours, 80 grams etc.
E.g. - Time spent in resolving is a CTQ for quick turnaround for customer query resolution. Resolution time is the metric used to measure how fast the resolution is provided
An application oriented question on the topic along with responses can be seen below. The best answer was provided by Mr Chandra on 7th September 2017.