Why is the input voltage on the label different from the input voltage in the spec? For example, the specification shows is 88~264 VAC while the label on the power supply says that it is 100~240VAC?

During safety verification process, the agency will use a stricter standard ±10% (IEC 62368 uses +10%, -10% for the product with AC input rated) of the input voltage range labeled on the power supply to conduct the test. So, operating at the wider input voltage range as specified on the spec. sheet should be fine. The narrower range of input voltage labeled on the power supply is to fulfill the test standard of safety regulation and make sure that users insert input voltage correctly.