We employ terahertz-range temperature-dependent Raman spectroscopy and first-principles lattice dynamical calculations to show that the undoped sodium ion conductors Na3PS4 and isostructural Na3PSe4 both exhibit anharmonic lattice dynamics. The anharmonic effects in the compounds involve coupled host lattice-Na+ ion dynamics that drive the tetragonal-to-cubic phase transition in both cases, but with a qualitative difference in the anharmonic character of the transition. Na3PSe4 shows an almost purely displacive character with the soft modes disappearing in the cubic phase as the change in symmetry shifts these modes to the Raman-inactive Brillouin zone boundary. Na3PS4 instead shows an order-disorder character in the cubic phase, with the soft modes persisting through the phase transition and remaining Raman active in the cubic phase, violating Raman selection rules for that phase. Our findings highlight the important role of coupled host lattice-mobile ion dynamics in vibrational instabilities that are coincident with the exceptional conductivity of these Na+ ion conductors.