The biggest source of confusion here is the terminology used by Airbus... Basicaly, "managed" means that navigation is done by the FMGC to keep the aircraft on a pre-programmed trajectory, while "selected" means that the pilot manually secects the desired heading/track and VS/FPA.
ILS approach is considered "managed", because the autopilot is actively tracking the Localizer and Glideslope. I suppose one could do an ILS approach "selected" - ie. using hdg/trk mode to follow the localizer and VS/FPA to follow glide slope, but there's no point in doing so, as it's a bit of a hassle. Either the APP mode is working, or you disconnect the autopilot and fly manually - it's much simpler.
LOC mode is oficially deemed "laterally managed, vertically selected", ie. the a/c follows the localizer automatically, while the pilot has to select the requred FPA to maintain descent path - as there is no glide slope (or it's not valid), the autopilot has nothing to "manage" vertically
VOR/NDB approaches can be flown fully "managed", ie. the autopilot is maintaining the aircraft on approach course and descent path using inputs from FMS and Baro Altimiter. This kind of guidance is, however, subject to several restrictions (waypoint coding, low temperature, single engine etc.). When "managed" is not allowed, one can do a "selected" approach, ie. use hdg/trk and vs/fpa to maintain the a/c on the radial and descend. Again, I have seen people doing VOR app managed/selected, ie. NAV mode for lateral navigation and FPA for vertical navigation, but it is not a SOP.