A "58 round" or "60 round" grip size refers to the inside diameter of the grip uninstalled.
Both 58 and 60 (referring to 0.58" and 0.60") sizes are considered standard sizes and most people consider the difference to be rather insignificant. Some grips only come in the 60R standard size. If you install the 58R grip on a 60R, it will be very slightly bigger (1/32") but most people cannot tell the difference.
The majority of golf grips come in only 60 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 58 (0.58"), 56 (0.56") or even 62 (0.62").
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