Zeke,

There is no short answer to your question, but here is the best answer:

The pitcher grade is used to give you a snapshot of a pitcher’s ability to get hitters out (Low OPS against---sum of opposing hitter’s slugging and on base percentage--- taking into account park and league effects). Some pitcher’s are very adept at getting hitters out but fail to get the key out which might get them out of an inning.
The clutch grade is used to mimic real life clutch performance as measured by ERA, inherited runners scored and blown saves. A pitcher with a pitching grade of 8 but a clutch rating of 5, describes a good pitcher with average performance based on his OPS against. If he were to have a clutch rating of 8 it would mean that his performance as measured by ERA and other performance stats would be higher than average for a pitcher graded at 8.