  The aim of this study is to better understand the connection between the
Lyman $\alpha$ rest-frame equivalent width (EW$_0$) and spectral properties as
well as ultraviolet (UV) continuum morphology by obtaining reliable EW$_0$
histograms for a statistical sample of galaxies and by assessing the fraction
of objects with large equivalent widths. We used integral field spectroscopy
from MUSE combined with broad-band data from the Hubble Space Telescope (HST)
to measure EW$_0$. We analysed the emission lines of $1920$ Lyman $\alpha$
emitters (LAEs) detected in the full MUSE-Wide (one hour exposure time) and
MUSE-Deep (ten hour exposure time) surveys and found UV continuum counterparts
in archival HST data. We fitted the UV continuum photometric images using the
Galfit software to gain morphological information on the rest-UV emission and
fitted the spectra obtained from MUSE to determine the double peak fraction,
asymmetry, full-width at half maximum, and flux of the Lyman $\alpha$ line. The
two surveys show different histograms of Lyman $\alpha$ EW$_0$. In MUSE-Wide,
$20\%$ of objects have EW$_0 > 240$ \r{A}, while this fraction is only $11\%$
in MUSE-Deep and $\approx 16\%$ for the full sample. This includes objects
without HST continuum counterparts (one-third of our sample), for which we give
lower limits for EW$_0$. The object with the highest securely measured EW$_0$
has EW$_0=589 \pm 193$ \r{A} (the highest lower limit being EW$_0=4464$ \r{A}).
We investigate the connection between EW$_0$ and Lyman $\alpha$ spectral or UV
continuum morphological properties. The survey depth has to be taken into
account when studying EW$_0$ distributions. We find that in general, high
EW$_0$ objects can have a wide range of spectral and UV morphological
properties, which might reflect that the underlying causes for high EW$_0$
values are equally varied. (abridged)
