Context. Based on their stellar parameters and the presence of a mid-IR excess due to circumstellar dust, RV Tauri stars have been classified as post-AGB stars. Our recent studies, however, reveal diverse spectral energy distributions (SEDs) among RV Tauri stars, suggesting they may occupy other evolutionary channels as well. Aims. The aim of this paper is to present the diverse SED characteristics of RV Tauri stars and investigate their evolutionary nature as a function of their SEDs. Methods. We carried out a systematic study of RV Tauri stars in the SMC and LMC because of their known distances and hence luminosities. Their SEDs were classified into three groups: dusty (disc-type), non-dusty (non-IR), and uncertain. A period-luminosity-colour (PLC) relation was calibrated. The luminosities from the PLC were complemented with those found using their SEDs and the stars were placed on a Hertzsprung-Russell diagram (HRD). I-band time series were used to search for period changes via (O−C) analyses to identify period changes. Results. The four main results from this study are: (1) RV Tauri stars with a clear IR excess have disc-type SEDs, which indicates that the dust is trapped in a stable disc. Given the strong link between disc-type SEDs and binarity in the Galaxy, we postulate that these are binaries as well. These cover a range of luminosities and we argue that the more luminous binaries are post-AGB stars while the lower luminosity binaries are likely post-red giant branch (post-RGB) stars. (2) Two of these objects have variable mean brightness with periods of 916 and 850 days, respectively, caused by variable extinction during orbital motion. (3) Non-dusty RV Tauri stars and objects with an uncertain SED evolve such that the circumstellar dust has dispersed. If they are single stars, they are post-AGB objects of low initial mass (<1.25 M_⊙), while if they are binaries, the low-luminosity portion of the sample are likely post-RGB stars. (4) We find that RV Tauri stars with dust are on average more luminous than the rest of the sample.