With a cashier’s check (assegno circolare), you can be sure the check is covered and you are getting the money; it’s like receiving cash; you can be sure you’ve been paid.
Because a cashier’s check is issued directly by the bank, which pre-checks the availability of funds in the bank account and blocks the funds correspondent to the check amount in the applicant’s bank account. Therefore, the applicant cannot issue the check and then spend the funds in his/her bank account. This way, the bank itself guarantees payment to the beneficiary, making the check a secure instrument, not subject to the risk of overdrafts.
A bank check (assegno bancario), on the other hand, is issued by the customer from their own checkbook in their current account. In this case, the bank isn’t even aware of the check and cannot guarantee coverage: payment depends on the actual availability of funds at the time of collection, i.e., whether they have not been spent yet. If there is insufficient funds in the bank account, the check may be overdrafted and not paid.