Like some sort of shared communication device that's larger, sits on a counter, and is plugged into the wall?

What a novel idea.

Fax machine? Genuinely not sure what you mean. Is the answer just "a computer" ?

Because while yes, that's true, this apparently recognises the different users. So presumably if a child is using it, that will be under managed parameters set by a parent - meaning that it's much harder for the child to circumvent.