Neutral kaons have two flavor combinations: $\mathrm{d}\bar{\mathrm{s}}$ and $\mathrm{s}\bar{\mathrm{d}}$. They can also be weak eigenstates: $\mathrm{\frac{d\bar{s} \pm s\bar{d}}{\sqrt{2}}}$.

But are neutral kaons of different compositions indistinguishable? If yes, how is it so, since they are composed of different fundamental particles? If not, what will happen when neutral kaon oscillates? They are suddenly indistinguishable when one oscillates into another? That indistinguishability can vary over time?