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We study qualitative aspects of the Welschinger-like $\mathbb Z$-valued countof real rational curves on primitively polarized real $K3$ surfaces. Inparticular, we prove that with respect to the degree of the polarization, atlogarithmic scale, the rate of growth of the number of such real rationalcurves is, up to a constant factor, the rate of growth of the number of complexrational curves. We indicate a few instances when the lower bound for thenumber of real rational curves provided by our count is sharp. In addition, weexhibit various congruences between real and complex counts.

Qualitative aspects of counting real rational curves on real K3 surfaces