By measuring the distance between closure systems, we can assess how closely two datasets or knowledge structures are related. In this paper, we propose distance functions for comparing closure systems, which can also be applied to concept lattices built on the same set of objects with varying attribute sets. Our proposed methods were implemented in the Go programming language. In our practical application, we examined industry maps from 63 school world atlases, originating from 23 countries and 40 publishers, from 1938 to 2018. We compare the distances between concept lattices constructed from three sets of map attributes: industrial sectors (13 attributes), power plants, pipelines, and material transport (12 attributes), and minerals (45 attributes). Our results demonstrate that the proposed distance functions could effectively capture structural differences between thematic layers of industrial maps, reflecting their varying conceptual complexity.