An IEC Class I power supply has an ac safety ground connection and thus is allowed to have only a single layer of insulation between the user and hazardous voltages. An IEC Class II power supply does not have an ac ground connection and uses double or reinforced insulation between the user and hazardous voltages.
A Class II power supply is an IEC rating for an ac-dc power supply which does not have an ac ground connection and uses double or reinforced insulation between the user and hazardous voltages. A class 2 power supply is an NEC label for a supply which has a limited power delivery capability and thus the wiring between the supply and the load presents less of a fire hazard.