Typically, a quality assurance group measures the process itself and makes adjustments to the process so as to achieve the optimum defect density warranted by the product and its market. The emphasis in quality assurance is to emplace defect prevention methods.
Testing is a quality control method, as are inspections.
The emphasis in quality control is to detect such defects as exist. The confusion arises because in many organizations, both jobs are done by the same group. In more process-mature organizations, however, the two jobs are distinct. It is a distinction made in the the broader quality assurance literature. These are goals to which we should aspire in software.