In targeted mode the drone collects the item, loads it in the cargo hold and expires. In area collect it will collect what it can, return each item in turn until it expires.
Drones will be the same, but the module that will lunch it will give different actions for drone (collect, prospect, fuel transfer).
For mining I'd expect people to use the area collect mode so it can collect as many chunks as possible. Targeted mode is when you have to grab something quickly.
This can be fired off to investigate an asteroid and determine its metal/mineral composition. Like all of the other drones (and limpets) each unit occupies a cargo slot and requires an appropriate module to control the type. So you need a cargo hatch breaker module and a collection drone controller to deploy either of those types of drone. The drones are universal and it is up to the controller to determine the actions of the launched drone.
Prospector drones only operate in targeted mode.