The shared SSL is installed globally on the server and all clients can use it. Its certificate is self-signed and is configured to work with Hostlantern server's name. That's why it will always show a pop-up warning when used.
On the other hand, the Private SSL is issued especially for your domain by a trusted authority. Browsers can validate the private SSL and will show a secure icon. Hostlantern definitely recommends the Private SSL for commercial projects.
