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.
"You cannot escape the responsibility of tomorrow by evading it today" -- Abraham Lincoln