There has been a substantial progress in the study of the Banach-Mazur distance between spaces of continuous functions over countable compact spaces in the last years. We survey the recent results and present a new contribution to the field. Also, extending the classical results of Bessaga and Pelczynski, we provide a classification of C(K) spaces over countable K by positive isomorphisms. Finally, we consider the related positive version of the Banach-Mazur distance between spaces of continuous functions, and we prove several new results in this direction. The talk is based on a joint preprint with M. Cuth, J. Havelka and B. Sari.