The main difference is the weight of the cabinet and the thickness of the steel used.
The scope of UL 291 is directed at the construction and security of the ATM when operated as intended by an authorized customer. The ATM must provide a limited degree of protection against unauthorized removal of currency. The records of the transactions must be made in order that the customer may be debited for currency dispensed. A limited degree of protection is required against the removal or manipulation of the records.
One is the Business Hours (BH) and the other is the 24-Hour Level-1 safe. Both must withstand attacks from someone trying to rob the currency or alter the records. Both have environmental requirements. And both have endurance requirements.