ICC ES Legacy Report ER-1952 mentions, “minimum spacing between lines [of nails] is 3/8 inch.”

The purpose of spacing a line of nails every 3/8 inch is to help minimize the potential of wood splitting. We’ve heard some inspectors are interpreting this 3/8 inch distance as the space needed between nail heads. We believe this interpretation is incorrect. The splitting of the framing caused by nails has very little to do with the size of the nail head, but is strongly influenced by the shank diameter of the nail.

Knowing this, the conclusion is that the 3/8-inch spacing is referring to the centerline-to-centerline spacing of the nail shank. It should also be noted that since some round nail heads are offset, it is not necessarily true that the 3/8-inch spacing is from centerline-to-centerline of the nail heads. If the nail’s head is symmetrical with the shank, then the centerline of the nail head and the centerline of the nail shank are identical.

You may also be interested in a related blog entry that covers staggering nails.