An e-commerce payment system facilitates the acceptance of electronic payment for online transactions. Also known as Electronic Data Interchange (EDI), e-commerce payment systems have become increasingly popular due to the widespread use of the internet-based shopping and banking.
There are numerous different payments systems available for online merchants. These include the traditional credit, debit and charge card but also new technologies such as digital-wallets, e-cash, mobile payment and e-checks. Another form of payment system is allowing a 3rd party to complete the online transaction for you. These companies are called Payment Service Providers (PSP), a good example is Paypal or WorldPay. (Note Paypal also offers its own payment system) Source : Wikipedia