What is the difference?

Quality Control vs. Quality Assurance

Quality Control is about controlling the quality. This is what the contractor accomplishing the work is responsible for. As the work is being performed, the contractor manages the work and controls the outcome of the work product. The contractor is responsible for the work being accomplished in accordance with the project specifications.

Quality Assurance is about assuring  the work the contractor controlled was accomplished in accordance with the project specifications. The contractor cannot assure quality in a unbiased manner, only a third party inspector can.