The term is also used more generally, to represent the idea that a new theory should reproduce the results of older well-established theories in those domains where the old theories work.

Sounds good to me, although that's not what I would have guessed from a name like 'correspondence principle'.

I suppose some minor difference is that this "law" is also applicable to meta-ethics, not just to physics. It's probably worth adding a link to the standard terminology to the LW wiki page.