Users are getting different behaviors when accessing different URLs as their virtual hosts

Issue

The environment is set up so that 2 different domains are acting as their virtual hosts
When a user accesses one domain and logs in, and then switches to the other domain name, they find that user sessions are not carried through to each URL

This is the intended behavior
User sessions and cookies are tied to the domain name, so when switching between different domain names and virtual hosts of the same environment, it is expected that the user would have to authenticate again
This is true as well for domain names that have a www pre-pended to it and the same name without the www prefix.
- For example: www.test.com and test.com are two separate domain names, and as such, user sessions would not be carried over between the two