For a start, let me clarify that by "almost identical configuration" I mean same volume, temperature and number of molecules (but different pressure). One could for instance take two identical systems of 1 mole of water each and following different paths of volume and temperature bringing them in liquid and solid state on both side of the phase transition such that the volume and the temperature of both systems are the same (thus with different pressure).
My question (if it makes sense) is: "How can we understand the fact that those systems with a structure that is so different (i.e. solid vs liquid) can have, in the same volume filled with the same number of molécules, the same temperature ? Do they have the same average translational kinetic energy ?" If yes, this is strange because a liquid is way more free to move than a solid and this tought-experiment is even more confusing when thinking about gas.