The address bar changes at checkout so that the checkout can be done via a secure connection. StoreSecured as a company only has the right to secure domains which end in our own url, ie yourstore.storesecured.com and our secure certificate is created for the same. During checkout the store automatically redirects the shopper to your secure subdomain, ie yourstore.storesecured.com.
The store will look exactly the same in secure mode, the only difference is that it is secured and the store address is slightly different. Most customers will not realize the URL has changed and will not be bothered by it because the look is still the same.