When it comes to grind size, there are three factors which make the biggest difference: contact time, extraction rate and flow rate.
Espresso
Espresso is a brewed through using pressure to force water through compacted coffee grounds. The contact time is very short, requiring an extra fine grind size.
Espresso Filter or Batch Brew
Espresso is a brewed through using pressure to force water through compacted coffee grounds. The contact time is very short, requiring an extra fine grind size.
Plunger or French Press
This is an immersion brewer. Water is added to coffee grounds and allowed to steep for several minutes before straining out the grounds. This method calls for a coarse grind setting.
Aeropress
It's similar to a French press. Recommended grind size is between medium and fine, depending on steep time.
Percolator or Mok Pot
Uses steam pressure to force water upwards through a filter basket full of coffee grounds. The contact time is quite short, but the pressure is a bit higher than your typical brewer. It calls for a medium grind size.