Many people, specially new to the PMI terminology get confused between Quality and Grade. They think that they are synonymous. However, there is a clear difference between quality and grade, and this often appears in PMP Exams as a question.
According to the PMBOK, 3rd Edition,
Quality is “The degree to which a set of inherent characteristics fulfills requirements”.
Grade is “a category or rank used to distinguish items that have the same functional use (e.g., “hammer”), but do not share the same requirements for quality (e.g., different hammers may need to withstand different amounts of force)”.
A Low Quality product or service is always a problem. But a Low Grade product may only mean that it does not have enough of the required features - it may be a scaled down version of a software.
If you take a diamond analogy, a high quality diamond may be based on the colour, or weight. If 2 high quality diamonds are found at the same place, one may be low grade and one high grade - depending on the number of impurities present inside each one even though they both adhere to the same quality.
Many a questions in the PMP exam will ask if low grade means low quality? And the answer is No.
The project manager and the project management team are responsible for determining and delivering the required levels of both quality and grade.
Hope this helps you. All the best in your PMP Exam preparations.