The Advanced Satellite for Cosmology and Astrophysics (ASCA) has made 22 observations on the Small Magellanic Cloud (SMC) by the end of the mission. We performed systematic analyses on all of these observation data and made comprehensive catalogues. We detected 106 discrete sources with a criterion of S/N >5. The source positions were determined with an ~40" error radius (90% confidence) for sources detected in the central 20' radius of the GIS. We detected coherent pulsations from 17 sources. Among them, eight were newly discovered during this study. We classified most of these pulsars as X-ray binary pulsars (XBPs) based on their properties such as flux variability. X-ray emission was detected from eight supernova remnants (SNRs). Among them, five SNRs showed emission lines in their spectra, hence we regarded the five as thermal. We find that XBPs and thermal SNRs in the SMC can be clearly separated by their spectral hardness ratio. Applying this empirical law to faint (thus unclassified) sources, we find 20 XBP candidates and four thermal SNR candidates. We find the spatial distributions of the XBPs and thermal SNRs (including candidates) resemble the distribution of young stars with ages ~ 2 x 10^7 yr. We compare the source populations in the SMC and in our Galaxy and discuss the star forming activity of the SMC.