  Context: Narrow-band surveys for Ly-alpha emitters (LAEs) is a powerful tool
in detecting high, and very high, redshift galaxies. Even though samples are
growing at redshifts z = 3 - 6, the nature of these galaxies is still poorly
known. Aims: To study the properties of z = 2.25 LAEs and compare those with
the properties of z > 3 LAEs. Methods: We present narrow-band imaging made with
the MPG/ESO 2.2m telescope with the WFI detector. We have made a selection for
emission-line objects and find 170 candidate typical LAEs and 17 candidates
which we regard as high UV-transmission LAEs. We have derived the magnitudes of
these objects in 8 bands from u* to Ks, and studied if they have X-ray and/or
radio counterparts. Results: We show that there has been significant evolution
in the properties of LAEs between redshift z ~ 3 and z = 2.25. The spread in
spectral energy distributions (SEDs) at the lower redshift is larger and we
detect a significant AGN contribution in the sample. The distribution of the
equivalent widths is narrower than at z ~ 3, with only a few candidates with
rest-frame equivalent width above the predicted limit of 240 A. The star
formation rates derived from the Ly-alpha emission compared to that derived
from the UV emission are lower by on average a factor of ~ 1.8, indicating a
large absorption of dust. Conclusion: LAEs at redshift z = 2.25 may be more
evolved than LAEs at higher redshift. The red SEDs imply more massive, older
and/or more dusty galaxies at lower redshift than observed at higher redshifts.
The decrease in equivalent widths and star formation rates indicate more
quiescent galaxies, with in general less star formation than in higher redshift
galaxies. At z = 2.25, AGN appear to be more abundant and also to contribute
more to the LAE population. [Abridged]
