We performed, for the first time, a season‐dependent geomagnetically quiet‐time climatology of mid‐ and low‐latitude ion densities during low and moderate solar flux conditions using Floating Potential Measurement Unit (FPMU) observations aboard the International Space Station (ISS) from 2008 to 2019. Our daytime observations indicate that the main characteristics of the equatorial ionization anomaly (EIA) at ∼400 km are consistent with those from other in situ and remote sensing probes. The FPMU daytime densities are also generally in good agreement with the corresponding results from the International Reference Ionosphere (IRI). However, the IRI does not reproduce the mid‐solar flux evening low‐latitude measured densities. In this period, the EIA exhibits strong longitude‐dependent crest‐to‐trough ratios and asymmetries due to the pre‐reversal enhancement (PRE) of the zonal electric field and thermospheric neutral winds. Our data also show strong structuring of the daytime and nighttime plasma densities. This includes a bulge, discussed for the first time here, in the EIA southern crest in the South Atlantic sector during the December solstice and equinox data, which we suggest being generated by the transport of plasma from the Weddell Sea anomaly (WSA). We also highlight and show the evolution of a midlatitude summer nighttime anomaly (MSNA) during the June solstice data in the North Atlantic sector. Our results give new insights into these two anomalies, where we show that they are stronger with increasing solar flux levels and that they last until the early morning. These latter results are not consistent with those from previous studies.