The concept of why a cookie created specifically for a particular domain cannot be accessed by another domain has been explained repeatedly year over year.
A lot of articles tried to explain, but in words, which can get a little complicating. (ok, maybe to me :>)
The following diagram explains it all. (yes, OpenSSO articles is still the to-go place for reading-up concepts)
Clear and precise. Why talk so much when a simple diagram can do the job? (maybe technical writers just like to write, but doesn't like to draw)
To introduce CDSSO, each SSO product implement its proprietary mechanism to support single sign-on across multiple domains.
OpenAM / OpenSSO introduced Cross-Domain Controller Servlet (CDCServlet) to handle CDSSO.
SiteMinder introduced Cookie Provider to handle the same scenario.