I agree that the distinction between the two depends on context. I think the usage of one term over the other would really depend on how it sounds, and not the actual, technical difference in meaning between the two. For instance, you could even say "...continuous rain..." and not change the conversational meaning. Something else you might consider, again, depending upon the context in which you're using this term, is saying "...constant rain...". To me, "...constant rain..." sounds a little more natural in a conversational context.