Via Tenting/Plugging
doesn't there need to be a wire that is fed through the via and soldered so as to create a conductive path between the bottom and top layers?


In professionally made boards, there's no wire passed through the hole. Instead, copper is electroplated onto the sides of the hole to make the connection.

The diagram you shared shows the plating has been done, leaving a copper connection through the board:



The plating process is done before solder mask is applied to the outer layers of the board, so the connection is already made before the tenting and/or plugging is done.


  Does it have to do with the size of the drill or are there external factors that must also be considered?


Tenting without plugging is not recommended for large hole sizes, because the air trapped in the hole will expand if the board is heated (for example, when soldering parts to the board), breaking the tenting.