To be pedantic, when I picked my handle back in the /. days, I thought it meant "a bijective homomorphism." Or, less opaquely, an invertible structure-preserving map (in the context of abstract algebra).

When I read about "isomorphic JavaScript" as, essentially, views rendered with the same code on the client or server (and yet a separate API), I can't help but think "You keep using that word. I do not think it means what you think it means."

Perhaps "symmetric JavaScript" would be better? But then the API is still an asymmetry...