The question is asked by many people so I decided to devote the post to explaining these terms. Let’s look at the standards first:

Quality Assurance (QA) is a part of quality management focused on providing confidence that quality requirements will be fulfilled. [ISO 9000]

Testing is a process consisting of all life cycle activities, both static and dynamic, concerned with planning, preparation and evaluation of software products and related work products to determine that they satisfy specified requirements, to demonstrate that they are fit for purpose and to detect defects. [ISTQB glossary]