Private SSL Certificate:
A private SSL Certificate uses your own domain. A private SSL should be used for protecting customer details, since the customer sees your domain rather than a 3rd party domain. The domain a private SSL uses will look something like "www.mywebsite.com".
Shared SSL Certificate:
A shared SSL Certificate isn't for a specific domain, they are used for servers that will, more than likely, be hosting more than one domain. Common uses for a shared SSL is when a company, for example, has a staff login page that the public doesn't see. The domain a private SSL uses will look something like "server.domain.com/~username/".
There is also a third type of SSL Certificate:
Self-Signed SSL Certificates:
A self-signed SSL certificate is generated by a server and isn't backed by an SSL provider. This can often generate a warning on most browsers. Common uses for this type of SSL is for encryption when verification isn't needed (within a business for example).
Please get in touch with our support team if you require further assistance.