The "Displacement Node" only works at render time (final rendering as well as in "Preview Rendering" mode) whereas the "Displacement Modifier" can already be seen working when modeling in "Solid" mode. Another difference is that the "Discplacement Node" uses greyscale "Bump Maps" pushing surface areas only up and down (and not sideways) whereas the "Displacement Modifier" has an "RGB to XYZ" mode which allows to create overhangs from a subdivided plane by using a color texture like for example the procedural "Noise" or "Voronoi" textures in their color versions:
