A gem quality diamond will exhibit a crisp, clear look to it. This is because its internal crystal structure is face-centered-cubic.
Moissanite is hexagonal, which means that it will not handle light the way a diamond does, and it creates what is termed "bi-refringance". Basically, light waves are split inside the crystal, and their velocity becomes unequal. Thus things appear doubled in appearance. The end result is that Moissanite does not look like a diamond when examined closely. Instead, it will appear fuzzy or blurry to the eye.
Diamond Hybrid® perfectly mimics the diamond's crystal structure (face-centered-cubic) resulting in a virtually identical look as fine diamond.
Moissanite has a different crystal structure. Hence it is cut to a different style than diamond to try and optimize its particular strengths. However, the different cut is also a key to the knowledgeable observer that it is not a diamond.
Moissanite under the H&A proportion scope
Diamond Hybrid® under the H&A proportion scope
Diamond Hybrid® is hand-cut to the highest diamond specifications possible (Hearts and Arrows), something which very few diamonds in fact will achieve (but they all strive for).