Ultraluminous supersoft sources (ULSs) are defined by a thermal spectrum with colour temperatures ∼0.1 keV, bolometric luminosities ∼ a few 1039 erg s−1, and almost no emission above 1 keV. It has never been clear how they fit into the general scheme of accreting compact objects. To address this problem, we studied a sample of seven ULSs with extensive Chandra and XMM–Newton coverage. We find an anticorrelation between fitted temperatures and radii of the thermal emitter, and no correlation between bolometric luminosity and radius or temperature. We compare the physical parameters of ULSs with those of classical supersoft sources, thought to be surface-nuclear-burning white dwarfs, and of ultraluminous X-ray sources (ULXs), thought to be super-Eddington stellar-mass black holes. We argue that ULSs are the sub-class of ULXs seen through the densest wind, perhaps an extension of the soft-ultraluminous regime. We suggest that in ULSs, the massive disc outflow becomes effectively optically thick and forms a large photosphere, shrouding the inner regions from our view. Our model predicts that when the photosphere expands to ≳ 105 km and the temperature decreases below ≈50 eV, ULSs become brighter in the far-UV but undetectable in X-rays. Conversely, we find that harder emission components begin to appear in ULSs when the fitted size of the thermal emitter is smallest (interpreted as a shrinking of the photosphere). The observed short-term variability and absorption edges are also consistent with clumpy outflows. We suggest that the transition between ULXs (with a harder tail) and ULSs (with only a soft thermal component) occurs at blackbody temperatures of ≈150 eV.