  We show that Modified Newtonian Dynamics (MOND) predict distinct galactic
acceleration curve geometries in $g2$-space - the space of total observed
centripetal accelerations $g_{\rm tot}$ vs the inferred Newtonian acceleration
from baryonic matter $g_{\rm N}$ - and corresponding rotation speed curves:
MOND modified gravity predicts cored geometries for isolated galaxies while
MOND modified inertia yields neutral geometries, ie. neither cuspy or cored,
based on a cusp-core classification of galaxy rotation curve geometry in
$g2$-space - rather than on inferred DM density profiles. The classification
can be applied both to DM and modified gravity models as well as data and
implies a {\it cusp-core} challenge for MOND from observations, for example of
cuspy galaxies, which is different from the so-called cusp-core problem of dark
matter (DM). We illustrate this challenge by a number of cuspy and also cored
galaxies from the SPARC rotation curve database, which deviate significantly
from the MOND modified gravity and MOND modified inertia predictions.
