Certified guarantees payment, while a bank draft is basically just a check (and funds are not guaranteed).
Since certified checks become the issuing bank's liability, banks will typically set the amount of money listed on the certified check aside in the holder's account so that there will always be an amount of money for the check. There are some downsides to using certified checks. For example, banks will usually charge a fee for certifying checks and that the depositor usually cannot place a stop payment order on a certified check.
A bank draft is a check drawn by one bank against funds deposited into its account at another bank, authorizing the second bank to make payment to the individual named in the draft. There may not be sufficient funds on the account with a bank draft, meaning there are no guarantees that the money is available for the payment.
The difference is in what legally happens behind the scenes. Cost differences depend on the banks and other factors.
A bank draft is a payment instrument between a
bank's agency and a merchant. Private individuals do not issue bank drafts, banks do. You ask the bank to issue a bank draft to a merchant and you pay the bank with your money. When a bank draft is received by the payee, they would send the draft back to the agency to verify and the bank would then give the money to the payee. Frequently, this is done when foreign currencies are involved, since it is not possible for personal checks (certified or not) to be issued in a currency other than that of the personal checking account. The bank would presumably have agencies that deal with the foreign currency involved, and you pay the bank according to the bank's conversion rates. Bank drafts are therefore commonly used for international transactions and are more popular outside the USA, where wire transfers and other similar services are preferred.
The bank would determine the fees associated with each. Certified checks are usually cheaper, although a comparison may not be informative since the two services are generally not substitutes for each other.