Enumerations of planar maps with various types of control on graph distances have been central to many results in random planar maps and their scaling limits. In this talk I will revisit some of these ideas focusing on distances between vertices on the boundary of a planar map. Following work of Bouttier and Guitter, several distance statistics are conveniently addressed in terms of orthogonal polynomials. Next, I will discuss an analogous combinatorial story around chord diagrams on the circle with control on crossing numbers, which received considerable attention in the physics literature recently in the context of holography and the DSSYK model. These stories turn out to be closely related by what one might, informally, think of as an example of "holography in combinatorics": the boundary metric of a bipartite planar map (i.e. the metric induced on the boundary contour of the map by its graph distance) is exactly encoded in a chord diagram, and, for special (non-probalistic) choices of face weights in the planar map, the boundary metric in this model coincides with the chord diagram model.