  We conducted a deep narrow-band imaging survey with the Subaru Prime Focus
Camera on the Subaru Telescope and constructed a sample of Ly$\alpha$ emitters
(LAEs) at z=2.53 in the UDS-CANDELS field where a sample of H$\alpha$ emitters
(HAEs) at the same redshift is already obtained from our previous narrow-band
observation at NIR. The deep narrow-band and multi broadband data allow us to
find LAEs of stellar masses and star-formation rates (SFRs) down to
$\gtrsim$$10^8$ M$_\odot$ and $\gtrsim$0.2 M$_\odot$/yr, respectively. We show
that the LAEs are located along the same mass-SFR sequence traced by normal
star-forming galaxies such as HAEs, but towards a significantly lower mass
regime. Likewise, LAEs seem to share the same mass--size relation with typical
star-forming galaxies, except for the massive LAEs, which tend to show
significantly compact sizes. We identify a vigorous mass growth in the central
part of LAEs: the stellar mass density in the central region of LAEs increases
as their total galaxy mass grows. On the other hand, we see no Ly$\alpha$ line
in emission for most of the HAEs. Rather, we find that the Ly$\alpha$ feature
is either absent or in absorption (Ly$\alpha$ absorbers; LAAs), and its
absorption strength may increase with reddening of the UV continuum slope. We
demonstrate that a deep Ly$\alpha$ narrow-band imaging like this study is able
to search for not only LAEs but also LAAs in a certain redshift slice. This
work suggests that LAEs trace normal star-forming galaxies in the low-mass
regime, while they remain as a unique population because the majority of HAEs
are not LAEs.
