  We have pointed out that the $SU(3)$ Yang-Mills theory has a new way of
reformulation using new field variables (minimal option), in addition to the
conventional option adopted by Cho, Faddeev and Niemi (maximal option). The
reformulation enables us to change the original non-Abelian gauge field into
the new field variables such that one of them called the restricted field gives
the dominant contribution to quark confinement in the gauge-independent way. In
the minimal option, especially, the restricted field is non-Abelian $U(2)$ and
involves the non-Abelian magnetic monopole. In the preceding lattice
conferences, we have accumulated the numerical evidences for the non-Abelian
magnetic-monopole dominance in addition to the restricted non-Abelian field
dominance for quark confinement supporting the non-Abelian dual
superconductivity using the minimal option for the SU(3) Yang-Mills theory.
This should be compared with the maximal option which is a gauge invarient
version of the Abelian projection in the maximal Abelian gauge: the restricted
field is Abelian $U(1) \times U(1)$ and involves only the Abelian magnetic
monopole, just like the Abelian projection.
  In this talk, we focus on discriminating between two reformulations, i.e.,
maximal and minimal options of $SU(3)$ Yang-Mills theory for quark confinement
from the viewpoint of dual superconductivity. For this purpose, we measure the
distribution of the chromoelectric flux connecting a quark and an antiquark and
the induced magnetic-monopole current around the flux tube.
