The moire pattern usually is visible when there is a textured surface on the chip over the inlay (as opposed to a smooth surface). The pattern on the overlay surface creates an optical interference with the dots in the half-tone screent used to print the inlay design, giving an impression of a third pattern. Depending on how the inlay is aligned with the pattern on the surface, you can see any of an infinite number of moire patterns. See the last issue Caesars Tahoe gold dollar chip for an example. I've seen 8 or 10 easily distinguishable patterns resulting from the differing alignment.

Most collectors don't consider these different varieties, any more than the differing alignment of a hotstamp marking with the edge inserts on a chip creates varieties.