  The Lyman-$\alpha$ (Ly$\alpha$) emission line has been ubiquitously used to
confirm and study high redshift galaxies. We report on the line morphology as
seen in the 2D spectra from the VIMOS Ultra Deep Survey in a sample of 914
Ly$\alpha$ emitters from a parent sample of 4192 star-forming galaxies at
$2<z_\mathrm{spec}\lesssim6$. The study of the spatial extent of Ly$\alpha$
emission provides insight into the escape of Ly$\alpha$ photons from galaxies.
We classify the line emission as either non-existent, coincident, projected
spatial offset, or extended with respect to the observed 2D UV continuum
emission. The line emitters in our sample are classified as ~45% coincident,
~24% extended and ~11% offset emitters. For galaxies with detected UV
continuum, we show that extended Ly$\alpha$ emitters (LAEs) correspond to the
highest equivalent width galaxies (with an average
$W_\mathrm{Ly\alpha}\sim-22${\AA}). This means that this class of objects is
the most common in narrow-band selected samples, which usually select high
equivalent width LAEs, $<-20${\AA}. Extended Ly$\alpha$ emitters are found to
be less massive, less star-forming, with lower dust content, and smaller UV
continuum sizes ($r_{50}\sim0.9$kpc) of all the classes considered here. We
also find that galaxies with larger UV-sizes have lower fractions of Ly$\alpha$
emitters. By stacking the spectra per emitter class we find that the weaker
Ly$\alpha$ emitters have stronger low ionization inter-stellar medium (ISM)
absorption lines. Interestingly, we find that galaxies with Ly$\alpha$ offset
emission (median separation of $1.1_{-0.8}^{+1.3}$kpc from UV continuum) show
similar velocity offsets in the ISM as those with no visible emission (and
different from other Ly$\alpha$ emitting classes). This class of objects may
hint at episodes of gas accretion, bright offset clumps, or on-going merging
activity into the larger galaxies.
