I hope others have given you a feel for the meaning. In some cases, they are totally unrelated.
Rolls Royce makes a quality car. How does purity apply at all in this case?
A chemical may be near 100% purity, but if it does not meet the required physical specifications (say granule size or bulk density) it is of poor quality.
"Strength does not come from physical capacity. It comes from indomitable will." -- Mahatma Gandhi