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]
(..) I WILL BE KING! Stick with me, and you'll never go hungry again! Yaay! All right! Long live the king! Long live the king! Long live the king! It's great that we'll soon be connected. With a king who'll be all-time adored. Of course, quid pro quo, you're expected To take certain duties on board (..)1994 The Lion King
(..) But, Dad, don't we eat the animal? Yes, Simba, but let me explain. When we die,our bodies become the grass. And the antelope eat the grass. And so, we are all connected in the great Circle of Life. Good morning, sire! Good morning, Zazu. Checking in... with the morning report. Fire away. (..)1994 The Lion King