I hate to be pedantic, but the form of the statements matter. So, if we may restate (1) and (2) in conditional form.
1. If rain is water dropping from the sky and it is raining, then water is dropping from the sky.
2. If rain is blood dropping from the sky and it is raining, then blood is dropping from the sky.
Both of these statements are equally true and convey equally no information.
(A real pedant would have written, "If (it is raining if and only if water is dropping from the sky) and it is raining, then water is dropping from the sky." But I'm not that pedantic, though I am pedantic enough to mention that this is what a pedant would do.)
But when e.g. a tornado sucks up frogs or fish from a body of water and they fall to the ground elsewhere, it is often referred to as raining frogs, or raining fish, or what have you, in a literal sense referring to the fall of the named animals from the sky during a storm accompanied by the contemporaneous fall of drops of water also (unlike the figurative expression raining cats and dogs, or the disco song about men).
So I'm not so sure it's correct to limit the term rain and derivatives thereof only to water falling. And that's even without considering other situations in which water falls from the sky without it being rain, e.g. a waterbomber in a firefighting situation, solid water (snow or hail), flood water falling off a cliff edge above, etc.