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]
(..) that smiIing motherf$cker. We shouId taIk to this Jewish guy, SeideIbaum, okay? He's got his own exchange. He charges % at the most. And he's connected. F$ck them. Mob guys. Guineas. I don't trust them. Did you sweep the house this month? The cars? Yeah, I toId you about it. (..)1983 Scarface