Your not the first to be confused. Motorcycle chains was earlier measured by pitch and width in inches. Since most people in the world are unfamiliar with thinking in fractions of an inch, a decimal looking system was introduced.

The first digit tells the pitch in eights of an inch. A 1/2" is now a 4xx and a 5/8" is now a 5xx chain.

The second and third digit tells width, also in eights of an inch. 1/4" becomes 2 eights, so x20. 5/16" becomes 2.5 eights, so a x25. A3/8" width becomes a x30.

So you are correct that your 1/2x5/16 chain is equal to a 525 chain.