Dash 8 Q400:
There are 2 navigation modes:
1/ "Blue needles", which is a colloquial term for basic navigation. Flight Guidance Computer (FGC) uses NAV/APP/BC mode and tracks via VOR/LOC/ILS input. No GPS input is involved. It's as if you are flying in your old 172 with steam driven gauges. The limitation is that in APP mode, there must be a DME associated with the VOR and in APP mode there are tighter steering tolerances. As a general rule it is not uncommon to see the aircraft wandering a little when in VOR mode compared to APP mode.
2/ FMS: In this mode the flight guidance computer is taking navigation input from the FMS. Depending on the software installation for the FMS, the FMS allows VOR, RNAV, and NDB approaches but not ILS approaches. In all cases LNAV is the navigation mode used so APP mode is never used. That said, the FMS itself has approach mode, but I won't go into that as it might just add to confusion! Normally, the FMS uses input from all sensors (ground and space based), but for a VOR approach it inhibits GPS input and uses only VOR input from the ground based aid on which the approach is based.
In practice we only use blue needles for ILS approaches and for all others we use FMS mode. Using FMS allows vertical gates to be used via VNAV, whereas in blue needles it is up to you to set vertical speed to not bust altitude limits throughout the approach. Only exception might be the rare situation where we have to do an NDB approach and the approach is not loaded in the FMS database.
For VOR and NDB approaches conducted in FMS mode, the pilot not flying selects their MFD (the navigation display) to blue needles so that the ground based aid input can be easily monitored.