  We compare the non-commutative quantum mechanics (NCQM) on sphere and the
discrete part of the spectrum of NCQM on pseudosphere (Lobachevsky plane, or
$AdS_2$) in the presence of a constant magnetic field $B$ with planar NCQM. We
show, that (pseudo)spherical NCQM has a ``critical point'', where the system
becomes effectively one-dimensional, and two different ``phases'', which the
phases of the planar system originate from, specified by the sign of the
parameter $\kappa=1-B\theta$. The ``critical point'' of (pseudo)spherical NCQM
corresponds to the $\kappa\to\infty $ point of conventional planar NCQM, and to
the ``critical point'' $\kappa=0$ of the so-called ``exotic'' planar NCQM, with
a symplectic coupling of the (commutative) magnetic field.
