I have been looking for an explanation of the two different chain sizes, the two vs three digit, and found it.
Chain size is in inches, the three digit number used to discribe the chain size is based on the "rule of eights". The first digit is for chain pitch. This is the distance between the pins. The second and third digits combine for roller width, with a decimal point inserted between the second and third digits.
For example, a 420 chain has a pitch of 4/8" = 1/2" (12.70mm) and a roller width of 2.0/8" = 1/4" (6.35mm).
A 525 chain (the size my bike uses) has a pitch of 5/8" (15.88mm) and a roller width of 2.5/8" (7.94mm).
A 530 chain has a pitch of 5/8" (15.88mm) and a roller width of 3.0/8" (9.52mm).
Now I feel better that anyone searching for "Chain size explanation" (including me) can find it for posterity. Thanks VifV!