My internet host says the reason why the session vars survive the move from HTTP to HTTPS is the way Coldfusion server is configured
"the default storage mechanism for client session data on our shared servers uses a sql database"
It is always disapointing that so many web hosting providers who offer ColdFusion do not actually understand the product.
The client scope and the session scope are two different things.
It is good that your hosting service has configured their system to store client data in the database rather then the registry (the default) or cookies. But as far as I know, you are not using any client scope variables.
Session scope variables always live in RAM. The factor that matters here is the cookies (CFID and CFTOKEN or JSESSIONID) that are sent between the server and the client so that the server can know which session variables belong to which clients. The way cookies work, is that they are associated with a specific domain name, thus if your https site uses a different domain (a pretty common configuration), then it will have different cookies which means different session scopes.