No. H2O is literally water. Water doesn’t have to only refer to the liquid mode. It is entirely accurate to say that ice and water vapor are essentially water in different states of matter.
This is a very chemical definition of water, and you are correct that it is coherent, but I don’t think it works because in a similar vein we could reduce everything to the subatomic level and make the case that everything is really just protons and neutrons in different modes and patterns.
In such a physical definition of matter, everything becomes a purely logical distinction, and language loses its power to convey the reality we clearly see. Ice is clearly different from water vapor, just as coal is different from diamonds, even if they are composed of the same material components. Therefore to call it all H2O and water is an inappropriate use of terms.
the Church’s position is that God is not a genus
I didn’t say that God was a genus. As a matter of semantics I submitted to the idea that the Trinity could be thought of as a genus, in order to show you that there can be real differences between the Persons of the Trinity, and that x is y but y is not x. It doesn’t have to be thought of in terms of a species and a genus though, here is a quote from Saint Augustine on the matter:
“We do not therefore use these terms according to genus or species, but as if according to a matter that is common and the same. Just as if three statues were made of the same gold, we should say three statues one gold, yet should neither call the gold genus, and the statues species; nor the gold species, and the statues individuals. For no species goes beyond its own individuals, so as to comprehend anything external to them. For when I define what man is, which is a specific name, every several man that exists is contained in the same individual definition, neither does anything belong to it which is not a man. But when I define gold, not statues alone, if they be gold, but rings also, and anything else that is made of gold, will belong to gold; and even if nothing were made of it, it would still be called gold; since, even if there were no gold statues, there will not therefore be no statues at all. Likewise no species goes beyond the definition of its genus. For when I define animal, since horse is a species of this genus, every horse is an animal; but every statue is not gold. So, although in the case of three golden statues we should rightly say three statues, one gold; yet we do not so say it, as to understand gold to be the genus, and the statues to be species.”