SmartSTORE works on any web site system that allows you to add JavaScript and HTML (which most do) and provides a checkout option on those platforms for Blackbaud Online Express, PayPal, Google Checkout and Amazon payments.
If you use a gateway other than Online Express no data is sent to RE automatically, the user can import sales from the payment providers reporting system i.e. PayPal give you a report on what has been sold.
SmartSTORE on Blackbaud web platforms (BBIS/BBNC) or that uses Online Express Checkout has closer integration and uses BBMS as it's payment option. Through this checkout the functionality is the same as above except the sale information is sent to RE/BBCRM via the relevant standard Blackbaud plugin (OLX, NetCommunity or Web Transactions) so it is 'integrated' with RE.