  Pulsar glitches are sudden increases in the spin frequency of an otherwise
steadily spinning down neutron star. These events are thought to represent a
direct probe of the dynamics of the superfluid interior of the star. However
glitches can differ significantly from one another, not only in size and
frequency, but also in the post-glitch response of the star. Some appear as
simple steps in frequency, while others also display an increase in spin-down
rate after the glitch. Others still show several exponentially relaxing
components in the post-glitch recovery. We show that if glitches are indeed due
to large scale unpinning of superfluid vortices, the different regions in which
this occurs and respective timescales on which they recouple can lead to the
various observed signatures. Furthermore we show that this framework naturally
accounts for the peculiar relaxations of glitches in Anomalous X-ray Pulsars.
