This illustration attempts to answer a question from our users about logging into a public google.com Google Account. You cannot as they are two different products. An account at Google Apps for your Domain is provided by your organization and is not the same* as an account at the public google.com set of applications and services.
Think of it this way: if your organization has a Microsoft Exchange server and another organization has a Microsoft Exchange server, can you use your organization’s username and password to login the other org’s Exchange server? Of course not! It’s the same product (Microsoft Exchange), but each organization represents a separate installation of that same product.
* Please note I am only addressing the ability to login and am not addressing issues of collaboration between google.com accounts and Google Apps for your Domain accounts. That’s coming in a future post.