I read in Necessity and Sufficiency that
For example, in graph theory a graph G is called bipartite if it is possible to assign to each of its vertices the color black or white in such a way that every edge of G has one endpoint of each color. And for any graph to be bipartite, it is a necessary and sufficient condition that it contain no odd-length cycles. Thus, discovering whether a graph has any odd cycles tells one whether it is bipartite and vice versa. A philosopher might characterize this state of affairs thus: "Although the concepts of bipartiteness and absence of odd cycles differ in intension, they have identical extension.
So, it looks like extension of equality. Isomorphism also looks like extension of equality. In programming languages and in math, I believe, we say that some objects are not equal (they are different instances) but they can be attributed to the same equivalence class. That is, they are equivalent.
Isomorphism says that you should use one equivalent object in one domain and another in the other domain. For instance, I should use 1 mile in UK and 1.609344 km in Europe, I speak about bipartite graphs in coloring and acyclic in some other context. Can I say that isomorphic objects are extensionally equivalent, that is, extension is basically an isomorphism? Both intentions and isomorphisms look like different aspects of the same entity, viewed from different angles for me.