When you purchase your own certificate, the customer will stay at your domain name during checkout. You also get your own secure symbol to put on your site (this comes from the provider, such as Network Solutions). If you get shared security, the link during checkout will change to MonsterCommerce. Here's what the shared security looks like:
https://xxxxx.monstercommercesites.com/index.asp?PageAction=CARTCHECKOUT&DC= where "xxxxx" is your MonsterCommerce account number.
Here's what your own security would look like on the first page of checkout: https://www.yourdomain.com/index.asp?PageAction=CARTCHECKOUT