Pulsars are a label we apply to neutron stars that have been observed to "pulse" radio and x-ray emissions. Although all pulsars are neutron stars, not all pulsars are the same. There are three distinct classes of pulsars are currently known: rotation-powered, where the loss of rotational energy of the star provides the power; accretion-powered pulsars, where the gravitational potential energy of accreted matter is the power source; and magnetars, where the decay of an extremely strong magnetic field provides the electromagnetic power. Recent observations with the Fermi Space Telescope has discovered a subclass of rotationally-powered pulsars that emit only gamma rays rather than in X-rays. Only 18 examples of this new class of pulsar are known.
While each of these classes of pulsar and the physics underlying them are quite different, the behaviour as seen from Earth is quite similar.
Since pulsars appear to pulse because they rotate, and it's impossible for the the initial stellar collapse which forms a neutron star not to add angular momentum on a core element during its gravitational collapse phase, it's a given that all neutron stars rotate.
However, neutron star rotation does slow down over time. So non-rotating neutron stars are at least possible. Hence not all neutron stars will necessarily be pulsars, but most will.
However practically, the definition of a pulsar is a "neutron star where we observe pulsations" rather than a distinct type of behaviour. So the answer is of necessity somewhat ambiguous.