a politically 'connected' businessman [=a businessman who has relationships with people who have political power]
In my mind, the two places 'are connected'. [=I think of the two places as being related to each other]
They 'are' somehow 'connected' to the royal family. [=they are related in some way to the royal family]
(..) this is our world. Oh, thank you. And this is another world. Normally, they're separate. But during the Alignment, everything is connected, all nine realms. All nine realms are passing through each other and gravity, light, and even matter, (..)2013 Thor: The Dark World