Kinetic Alfvén waves (KAWs) are the short-wavelength extension of the magnetohydrodynamics Alfvén-wave branch in the case of highly oblique propagation with respect to the background magnetic field. Observations of space plasma show that small-scale turbulence is mainly KAW-like. We apply two theoretical approaches, a collisional two-fluid theory and a collisionless linear kinetic theory, to obtain predictions for the KAW polarizations depending on β p (the ratio of the proton thermal pressure to the magnetic pressure) at the ion gyroscale in terms of fluctuations in density, bulk velocity, and pressure. We perform a wavelet analysis of Magnetospheric Multiscale magnetosheath measurements and compare the observations with both theories. We find that the two-fluid theory predicts the observations better than the kinetic theory, suggesting that the small-scale KAW-like fluctuations exhibit a fluid-like behavior in the magnetosheath although the plasma is weakly collisional. We also present predictions for the KAW polarizations in the inner heliosphere that are testable with Parker Solar Probe and Solar Orbiter.