What I'm thinking is: if two conlangs have the same syntactical structure and can be translated by simply exchanging words while maintaining the same (or very similar) structure, is there are specific term for this scenario, and are there any examples for this? I'd imagine Lojban and Loglan would probably fit in this category as Lojban is, after all, a child project of Loglan. Are there any other examples of conlangs designed with identical (or very similar) syntactic features, and is there a name for this relationship?
There is the term relexification meaning that the words of a given language are replaced by new words without changing the structure of the starting language. Relexification does not only occur in conlangs but also in natural languages.
For a lower-level kind of isomorphism: I have read a story in which an alien speaks a synthetic language, suited to its own vocal tract, into a machine that converts its speech phoneme-for-phoneme into a human language.
It could be a scene in Poul Anderson's A Circus of Hells, or not.