We present the classification of 717 radio-continuum sources from the Australia Telescope Compact Array Catalogue of the Small Magellanic Cloud (SMC). These sources have been categorized into one of three groups: supernova remnants (SNRs), HII regions and background sources. In total, we name 71 sources as HII regions (or candidates) and 21 sources as SNRs (or candidates) within the SMC. Six sources are named as either HII regions or background sources. Two sources are candidate radio planetary nebulae and one additional source is coincident with an X-ray binary, all also located within the SMC. We classify 616 objects as background sources and present their statistics.