On Mars, so-called “scalloped depressions” are widely observed in Utopia Planitia (UP) and Malea Planum (MP). Typically, they are rimless, metres- to decametres-deep, incised sharply, tiered inwardly, polygonised and sometimes pitted. The depressions seemingly incise terrain that is icy and possibly thermokarstic, i.e. produced by the thermal destabilisation of the icy terrain. Agewise, the depressions are thought to be relatively youthful, originating in the Late Amazonian Epoch. Here, we report the presence of similar depressions in the Argyre region (AR) (30–60° S; 290–355° E). More importantly, we separate and differentiate these landforms into two groups: (ice-rich) periglacial depressions (Type-1); and, (icy) glacial depressions (Type-2a-c). This differentiation is presented to the Mars community for the first time. Based on a suite of morphological and geological characteristics synonymous with ice-complexes in the Lena Peninsula (eastern Russia) and the Tuktoyaktuk Coastlands (Northwest Territories, Canada), we propose that the Type-1 depressions are ice-rich periglacial basins that have undergone volatile depletion largely by sublimation and as the result of thermal destabilisation. In keeping with the terms and associated definitions derived of terrestrial periglacial-geomorphology, ice-rich refers to permanently frozen-ground in which ice lenses or segregation ice (collectively referenced as excess ice) have formed. We suggest that the depressions are the product of a multi-step, cold-climate geochronology: Atmospheric precipitation and surface accumulation of an icy mantle during recent high obliquities. Regional or local triple-point conditions and thaw/evaporation of the mantle, either by exogenic forcing, i.e. obliquity-driven rises of aerial and sub-aerial temperatures, or endogenic forcing, i.e. along Argyre impact-related basement structures. Meltwater migration into the regolith, at least to the full depth of the depressions. Freeze-thaw cycling and the formation of excess ice. Sublimation of the excess ice and depression formation as high obliquity dissipates and near-surface ice becomes unstable. The Type-2 depressions exhibit characteristics suggestive of (supra-glacial) dead-ice basins and snow/ice suncups observed in high-alpine landscapes on Earth, e.g. the Swiss Alps and the Himalayas. Like the Type-1 depressions, the Type-2 depressions could be the work of sublimation; however, the latter differ from the former in that they seem to develop within a glacial-like icy mantle that blankets the surface rather than within an ice-rich and periglacially-revised regolith at/near the surface. Interestingly, the Type-2 depressions overlie the Type-1 depressions at some locations. If the periglacial/glacial morphological and stratigraphical dichotomy of depressions is valid, then this points to recent glaciation at some locations within the AR being precursed by at least one episode of periglaciation. This also suggests that periglaciation has a deeper history in the region than has been thought hitherto. Moreover, if the hypothesised differences amongst the Argyre-based depressions are mirrored in Utopia Planitia and Malea Planum, then perhaps this periglacial-glacial dichotomy and its associated geochronology are as relevant to understanding late period landscape-evolution in these two regions as it is in the AR?