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), H II regions and background sources. In total, we name 71 sources as H II regions (or candidates) and 21 sources as SNRs (or candidates) within the SMC. Six sources are named as either H II 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.