ShopSite can use a secure SSL URL if provided one in the configuration, however the actual SSL services must already be functioning on your web server, so the SSL certificate is a hosting issue, not a ShopSite issue. If your ShopSite was already configured to use an SSL URL when you got it, then it is likely that your host set this up for you, and is likely that the SSL URL is through their shared domain name.
Some hosts might provide something like
https://secure.theircompany.com/~youraccount, some might have something like
https://youraccount.theircompany.com, etc, there are many different ways to do this. But the bottom line is generally that unless you purchase your own SSL certificate, your hosts' secure domain name is always going to be in your SSL URLs. For some merchants this is fine, but some (especially as their online sales increase) may feel it is worth a few hundred bucks to keep their own domain name throughout the checkout process.
It's a personal choice. But the actual communication of the data over the web is secure either way, whether it be a shared SSL URL or your own.
-Loren