Stuck in an ATR, some of the information is not quite correct.
ILS and LOC/DME approaches are not managed.
Managed modes on the Airbus are related to climbs, descents and approaches.
As has been touched on here, a managed approach is one that is flown using the the data in the FMGC. This data or coding, allows the aircraft to be flown along a lateral and vertical profile which should represent the profile of the approach plate of a non precision approach, taking into consideration the altitude and speed constraints. When the aircraft is flown in this manner the flight mode annunciator (FMA) will display APP NAV FINAL blue as the aircraft flies along the lateral profile of the approach. Once the aircraft reaches the FAF, FINAL APP mode will engage and the aircraft will fly the vertical and lateral profile of the approach. This is referred to as a fully managed approach.
The beauty of this type of approach is that the aircraft does not even need a beacon to navigate with, as all the data is stored in the FMGC. All this information is in the flight crew operating manual.
Of course the aircraft can be flown like any other, using raw data. This is typically done using selected modes, i.e. the pilot selecting headings/tracks and vertical guidance through the flight control unit. This would be referred to as a fully selected approach.
Going back to precision approaches, the reason they are not referred to as managed approaches is because the aircraft is navigating using a glide slope and localizer transmitter, not the data in the FMGC.
Hope that helps.