There’s no confusion, but there’s a different understanding of SSO.
Again, there is a difference between shared credentials and shared sessions. While the former is clearly desirable, the latter can be dangerous. In your example above, while logging into one service, you’re logged into a (hidden/invisible) second service automatically and unknowingly, which in turn prevents you from logging out of the first service effectively. By effectively I don’t mean the session itself (yes, you are logged out) but the missing necessity of entering the credentials again on re-login. This is a security issue when using public computers as your credentials are still kept alive, despite you having logged out of the very single service you logged into previously.
Not really. Ideally the two services would be entirely decoupled in terms of their session handling and credential buffering - they should only share the same credential database. This way one could use two totally independent services (one doesn’t influence the other in any way) with a single account. That’s what SSO is supposed to do IMHO. However, if the only way to implement this is to always log out of every service when logging out of one, then that’s still way better (read: more secure) then the current implementation.