  We study current-induced dynamics of a magnetic domain wall by solving a
time-dependent Schr\"{o}dinger equation combined with Landau-Lifshitz-Gilbert
equation in a one-dimensional electron system coupled to localized spins. Two
types of domain-wall motions are observed depending on the hard-axis
anisotropy, $K_{\perp}$, of the localized spin system. For small values of
$K_{\perp}$, the magnetic domain wall shows a streaming motion driven by spin
transfer. In contrast, for large values of $K_{\perp}$, a stick-slip motion
driven by momentum transfer is obtained. We clarify the origin of these
characters of domain-wall motions in terms of the dynamics of one-particle
energy levels and distribution functions.
