With respect to American Express, they operate are their own closed system. American Express functions as issuing bank, payment processor and merchant acquiring bank. American Express has had the reputation of providing the best service and protection to users and merchants; but they also charge the highest fees.
Visa, MasterCard and Discover all use the same clearing process run by third party banks and service providers.
Direct Debits
Payment processors can also process "direct debits" charging the purchaser's bank account and depositing the funds into the seller's bank account. This transaction method is less common. Direct debits are used primarily for subscription based services; and are usually done when the purchaser is unlikely to cancel the service, e.g., a utility bill. Fees to the
merchant services sales training are usually lower, often running at 1% or less.