  We show that spinor Bose gases subject to a quadratic Zeeman effect exhibit
coexisting superfluidity and spin superfluidity, and study the interplay
between these two distinct types of superfluidity. To illustrate that the basic
principles governing these two types of superfluidity are the same, we describe
the magnetization and particle-density dynamics in a single hydrodynamic
framework. In this description spin and mass supercurrents are driven by their
respective chemical potential gradients. As an application, we propose an
experimentally accessible stationary state, where the two types of
supercurrents counterflow and cancel each other, thus resulting in no mass
transport. Furthermore, we propose a straightforward setup to probe spin
superfluidity by measuring the in-plane magnetization angle of the whole cloud
of atoms. We verify the robustness of these findings by evaluating the
four-magnon collision time, and find that the time scale for coherent
(superfluid) dynamics is separated from that of the slower incoherent dynamics
by one order of magnitude. Comparing the atom and magnon kinetics reveals that
while the former can be hydrodynamic, the latter is typically collisionless
under most experimental conditions. This implies that, while our
zero-temperature hydrodynamic equations are a valid description of spin
transport in Bose gases, a hydrodynamic description that treats both mass and
spin transport at finite temperatures may not be readily feasible.
