In general conversation, we use quality and grade interchangeably. But they are not the same as far as Project Quality Management is concerned.
Quality of a product is “the degree to which a set of inherent characteristics fulfill requirements”
–American Society for Quality, 2000 standards
Grade is something related to classification of products or services based usually on technical specifications. Grade is based on Scope & not on quality. Example: Various grades of Construction Cements like 33 Grade, 43 Grade , 53 Grade, etc. are available in market.
Different graded items are created with a purpose or requirement and low grade does not mean it is a defective one or low quality one. But low quality product means the product is not meeting requirement and it is defective. And any grade can have defects if it does not meet the requirement.
In software development, limited feature(usually called as demo applications) release and full feature (usually called as full license) release – both can be considered as two different grades of products and not low quality one.
Project manager & the project management team decides the required levels of quality and grade of the product.