This paper is in the formal concept analysis framework, an algebraic hierarchisation method of data based on the notion of extent/intent, i.e. of maximally shared attributes and objects. Here we present a correspondence-based similarity measure between two formal concept lattices, and compare it to results of a previous paper which introduced a structure-based dissimilarity measure. We define an expressive model using correspondences between objects and between attributes of the two lattices. A key point of our approach is that the correspondences may not be mappings and may associate each object (resp. attribute) of one lattice with several objects (resp. attributes) of another one.