Aren't classical, identical particles, always indistinguishable?
Consider monitoring the trajectory of one particle. After it collides with an identical particle how would one continue to keep track of which particle is which? However, textbooks on statistical mechanics routinely discuss classical, identical (but distinguishable) particles in the context of the Gibbs Paradox (https://en.wikipedia.org/wiki/Gibbs_paradox) and other situations.
Following query does not address the issue: Distinguishing identical particles