I don’t think that a person can be „plugged into“ anything. It’s simply the wrong word combination. A wire or electrical connection can be plugged into something, but those are the limitations of the phrase. It’s fairly literal and, as far as I know, never used in a figurative sense. Connected to something can have both a literal and figurative meaning. That’s the difference. So, an electrical device can be connected to an electrical outlet, but at the same time one person can feel connected to another person, or culture. So, „connected“= either literal or figurative meaning. „plugged into“= only literal meaning.

They’re very similar, “plugged in” has a more physical implication, it conveys the idea of being physically attached to something like with a cord or wires. If you are “connected to” something, that can be more of a non-physical thing, for example you could be connected to the internet (since the internet isn’t a physical object) but your phone would be plugged into the outlet or charger (a physical object). Or, you could be connected to person, because that’s talking about a relationship which is not a physical object but more of a concept

Sorry for the typos. There’s some editing function on the board that I haven’t figured out yet.