I guess there is more than one "correct" way to measure group size, but usually you want the greatest distance between any two holes, center to center. To obtain that, its easiest to measure between the outside edges of the holes, then subtract one bullet diameter.

Therefore, a 1/2" group with 50 cal bullets would essentially look like one 1" diameter hole. A 1" group (discounting tearing of the target) would theoretically have 1/2" of space between the inside edges of the holes.

Minute of angle (MOA) is a term used to describe the measure of the actual angle you would get if you drew lines from two holes in the target, back to the muzzle. The lines would be pretty close to parallel, but would of course intersect at the muzzle. That's where you'd measure the angle. With a 1" group, that angle would measure about 1/60th of a degree, or one minute of one degree of angle.

I have no idea what 1/2" moa is.