  We compare the physical and morphological properties of z ~ 2 Lyman-alpha
emitting galaxies (LAEs) identified in the HETDEX Pilot Survey and narrow band
studies with those of z ~ 2 optical emission line galaxies (oELGs) identified
via HST WFC3 infrared grism spectroscopy. Both sets of galaxies extend over the
same range in stellar mass (7.5 < logM < 10.5), size (0.5 < R < 3.0 kpc), and
star-formation rate (~1 < SFR < 100). Remarkably, a comparison of the most
commonly used physical and morphological parameters -- stellar mass, half-light
radius, UV slope, star formation rate, ellipticity, nearest neighbor distance,
star formation surface density, specific star formation rate, [O III]
luminosity, and [O III] equivalent width -- reveals no statistically
significant differences between the populations. This suggests that the
processes and conditions which regulate the escape of Ly-alpha from a z ~ 2
star-forming galaxy do not depend on these quantities. In particular, the lack
of dependence on the UV slope suggests that Ly-alpha emission is not being
significantly modulated by diffuse dust in the interstellar medium. We develop
a simple model of Ly-alpha emission that connects LAEs to all high-redshift
star forming galaxies where the escape of Ly-alpha depends on the sightline
through the galaxy. Using this model, we find that mean solid angle for
Ly-alpha escape is 2.4+/-0.8 steradians; this value is consistent with those
calculated from other studies.
