There is no much difference between Visa as used in Credit Carda and Visa Electron as used in Debit Cards. The only difference, if I can put it in Telco speak, one is post-paid and the other one is pre-paid.

They all use the same Visa platform to operate. Banks can choose to enable their cards for over the internet transaction or not. They can also limit the countries where you can carry out these transaction.

Most bank allow you to transact over the internet with the cards, but some like Standard Chartered have recently disable this feature. It is better to contact your bank and find out more about their cards.