They are syntactically different but semantically equivalent.

A plane graph is said to be self-dual if it is isomorphic to its dual graph.

Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may be identified.

In informal contexts, mathematicians often use the word modulo (or simply "mod") for similar purposes, as in "modulo isomorphism".

Isomorphism itself is not purely a JavaScript thing. You can also build an isomorphic application in Dart or even use two different languages/stacks to render the same result. In fact there are many “isomorphic” applications which render a full HTML document on the server using PHP, Java or Ruby and use JavaScript and AJAX to create a rich user experience in the browser. This was the way things were done before the rise of Single Page Applications. The only real reason isomorphism is tied to JavaScript is because it’s the only language widely supported in the browser, and so at least part of the whole thing will use JavaScript. There’s no such thing as Isomorphic JavaScript, only isomorphic applications.

Isomorphism in my mind simply refers to the fact that the web application can be rendered on multiple platforms (in the browser and on the server).

Isomorphism in the context of globalization, is an idea of contemporary national societies that is addressed by the institutionalization of world models constructed and propagated through global cultural and associational processes.

morphisms,