I highly recommend reading the aforementioned threads as well. My "Fielding for dummies" explanation is "Fielding grade tells you how many errors he'll commit", while "range grade tells you how many hits he'll take away". As others have mentioned, not every letter grade is created equal. But if while searching for players you click on their name, and you look at "performance history", take a look at their Fielding history and pay attention to errors and +/- plays.
A "-" play means it would have been an out, but due to the players range stat, it became a hit, whereas a "+" play means it would have been a hit, but due to the players range stat it became an out. Two players may both have defense grades of C/A+, where one player commits an average of 30 Errors with 20 + plays (a net -10), where the other player commits an average of 50 errors with only 5 + plays.