What's the difference between a double chain ring and a compact chain ring?

BBC on a Std road cranks double is 130mm compact is 110mm.
This is distance from bolt to bolt center to center.

The BCD Bolt Circle Diameter for most modern cranksets, including Shimano are 130 mm. Compact cranksets have a 110 mm BCD and can accept smaller chainrings. Campagnolo standard cranksets have a 135 BCD.

Of course to complicate things the TA cranks on my bikes have a BCD (50.4 mm) that's less than half the size of the current 'compacts' but they're considered regular size.

And to JTGraphics:
No, the BCD is the diameter of a circle that would pass through the center of the bolts. The center-center distance between bolts is 76.4mm for a 130mm BCD and 64.7mm for a 110mm BCD.

On the off chance you meant compact crankset instead of an individual chainring, the idea is to give you a lower/wider gear range without going to a triple. The size difference between the rings will be greater and the size of the rings themselves will be smaller than on a more standard double.

How about this, a compact crank usually has two chainrings,in the 48 and 34 range, while a standard usually has them in the 52 and 42 range. Give or take a tooth or two...

A "standard" road bike double is typically a 53/39. A "compact" road bike double is typically 50/34.

A compact crankset is a double crankset. Not all double cranksets are compact cranksets. The cyclocross crank (46/38) on my hybrid is neither a compact not a standard road double.

And they make great "compact" cranks (43/30 in this case):

Lyotard pedals!!!!