Revealing the formation, dynamics, and contribution to plasma heating of magnetic field fluctuations in the solar wind is an important task for heliospheric physics and for a general plasma turbulence theory. Spacecraft observations in the solar wind are limited to spatially localized measurements, so that the evolution of fluctuation properties with solar wind propagation is mostly studied via statistical analyses of data sets collected by different spacecraft at various radial distances from the Sun. In this study we investigate the evolution of turbulence in the Earth’s magnetosheath, a plasma system sharing many properties with the solar wind. The near-Earth space environment is being explored by multiple spacecraft missions, which may allow us to trace the evolution of magnetosheath fluctuations with simultaneous measurements at different distances from their origin, the Earth’s bow shock. We compare ARTEMIS and Magnetospheric Multiscale (MMS) Mission measurements in the Earth magnetosheath and Parker Solar Probe measurements of the solar wind at different radial distances. The comparison is supported by three numerical simulations of the magnetosheath magnetic and plasma fluctuations: global hybrid simulation resolving ion kinetic and including effects of Earth’s dipole field and realistic bow shock, hybrid and Hall-MHD simulations in expanding boxes that mimic the magnetosheath volume expansion with the radial distance from the dayside bow shock. The comparison shows that the magnetosheath can be considered as a miniaturized version of the solar wind system with much stronger plasma thermal anisotropy and an almost equal amount of forward and backward propagating Alfvén waves. Thus, many processes, such as turbulence development and kinetic instability contributions to plasma heating, occurring on slow timescales and over large distances in the solar wind, occur more rapidly in the magnetosheath and can be investigated in detail by multiple near-Earth spacecraft.