difference between 'real time' payment gateway and not real time?

I am new to this subject,but I have researched it and read through tutorial and internet and want to know if there are any advantages to use not 'real time' payment gateway ?...It seems it is much cheeper and offers u full control of the process:unsure:

The way I use the term, a 'real-time' payment gateway would be a regular merchant account, or something like Paypal or Google Checkout, which accepts your customer's payment as he is checking out.

The opposite would be the Offline Credit Card module (now removed from Zencart and not recommended) where the credit card details are sent to you and you use a physical CC terminal sometime after the customer checks out to process the payment. You still need a merchant account with a bank, so there may not be any savings.

I, for one, would not buy from you if I know that you use the Offline module, for security reasons.