  We consider the off-lattice two-dimensional $q$-state active clock model
(ACM) as a natural discretization of the Vicsek model (VM) describing flocking.
The ACM consists of particles able to move in the plane in a discrete set of
$q$ equidistant angular directions, as in the active Potts model (APM), with an
alignment interaction inspired by the ferromagnetic equilibrium clock model. We
find that for a small number of directions, the flocking transition of the ACM
has the same phenomenology as the APM, including macrophase separation and
reorientation transition. For a larger number of directions, the flocking
transition in the ACM becomes equivalent to the one of the VM and displays
microphase separation and only transverse bands, i.e. no re-orientation
transition. Concomitantly also the transition of the $q\to\infty$ limit of the
ACM, the active XY model (AXYM), is in the same universality class as the VM.
We also construct a coarse-grained hydrodynamic description for the ACM and
AXYM akin to the VM.
