A "580 (or 58)" or "600 (or 60)" grip size refers to the inside diameter of the grip uninstalled.
Both 580 and 600 (referring to 0.580" and 0.600" respectively) core sizes are considered standard sizes and most people consider the difference to be rather insignificant. Note that core size is different from outer diameter size. The core size is the INSIDE diameter of the grip and usually has little or no correlation to the OUTSIDE diameter of the grip (which is typically denoted with the sizing terms "Standard", "Midsize", "Oversize", etc.). Some grips only come in the 600 standard core size. If you install the 580 grip on a 0.600" butt diameter shaft, it will be slightly bigger (+1/32") than installing a 600 grip, but most people cannot tell the difference either way.
The majority of golf grips come in only 600 core diameter size. This size most closely matches the majority of all outer butt diameter shaft sizes. Some grips however come in additional core sizes, like 580 (0.580"), 560 (0.560"), 500 (0.500") or even 620 (0.620").
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