办手续是第一次去办 补手续是已经办过了 但是有问题 需要再补充一下

you are supposed to say how to distinguish "补办手续" and "办手续" cuz 补手续 is not that much natural,then i will tell you that 补办手续 means you missed it before and now you need to fix it up but 办手续 means you want to do it now ,and it just highlight what you are doing now and we don't know whether you missed it or not before

办手续是以前没有办过手续，第一次去办手续，补手续是在以前办过手续，担因遗失或缺少某些证件而去再次办理手续

補 : 添足所缺少的。 如：「補充」﹑「填補」﹑「添補」。 國語˙越語上：「去民之所惡，補民之不足。」 補(補正)手續 : 原先辦理的手續不完備 如 證件不齊全 未簽名 逾期等因素 致使文件 或 程序 不生合法效用 須就缺失加以補正 稱 補(補正)手續 辦手續 : 依規定的文件或程序處理事情