Tests for nonnested models (Vuong, Clarke)

When comparing generalized linear models, do the Vuong and Clarke tests require that the response distributions be the same? For example, could I use them to compare a gamma model with an inverse gaussian model? Are such models, with same or differing predictors, considered nonnested but meet the assumptions of these tests? I've tried looking at Vuong's highly theoretical papers and Clarke's somewhat more approachable papers, but the answer to this is not clear to me.

I'd appreciate a citation that makes this clear rather than speculation.