Monster Manuals are not the first time people have built elaborate taxonomies of the monstrous. The medieval bestiary (also not the first on the job, but well ahead of the monster manual) presents us with an earlier example of the cataloging and categorizing of monsters and animals and all their features. Take a look at a medieval bestiary, the source (albeit often mediated by literature) of some of D&D's core monsters. The urge to catalog, to categorize, to create a taxonomy, to explain -- the creative and exploratory instincts of man -- are on full display. But the results are very different than those of the modern monster manual.
In OD&D and throughout some of the life of 1st edition, monsters were, broadly speaking, things that you meet. You encounter them. Some of them will talk. Some will fight. Some will chase you. Others want to be left alone. Some are puzzles. Some are traps. Some are dirty tricks Gary came up with to punish you for rummaging around in corpses or listening at doors. Their roles are varied, except that they are out there, some sitting in rooms or living in lairs, some wandering about, but all there to be encountered, if you're in the right place at the right time.
Somewhere by the end of 1st edition, monsters were already taking on a life of their own beyond the encounter. Ecological naturalism was taking over, and monsters were increasingly becoming races and beings that lived and loved and died, with or without you. By this time, it doesn't raise an eyebrow to talk about the "typical" minotaur or "typical" medusa, or typical anything (pretty much): beings which were originally uniquely monstrous (or very nearly so) had become species. No more or less natural (within a magical world) than a dog or a cat. Monsters by convention, but essentially ordinary.
By 3rd edition many monsters were ready for a bit of reinvention: both the new art direction and in some cases the new stats gave us new angles on old monsters, or at least more consistent stats for the monstrous, with reduced information about ecology and lifestyle but no major changes. By 4th edition, consistency within the game rules was taking over, and it was time to reinvent and reimagine monsters once again. One part of this was the attempt to make the monster trademarkable and copyrightable and ownable. The monster needed to become intellectual property, something owned by Wizards of the Coast and by extension Hasbro. The Flame Blitz Shadow Orc isn't the result of Wizards's tin ear. It's a business move. Alongside this came another move, with the goal to reinvent the monsters, systematize them in a new overarching story/context (with primordials and titans), and in some ways an attempt to make the monster a monster again.
Unfortunately, 4th edition missed the mark on monsters. The 4e monster is not something that exists separately from the PCs, as was the monster of 2nd edition. And it is not even something that exists to be met, to be encountered, as it had been earlier yet. Rather, the monster is something to be fought. You don't encounter a 4th edition monster, you fight it. It does not frighten you, it does not chase you, it is not hiding under your bed. It may be a puzzle on some level, but it is mainly a combat puzzle. A monster is something you fight.
There's something right about that, the fighting monsters part. That is one of the things you do with monsters in myth and legend. But that isn't everything you do with them, even if you're a hero, and it certainly isn't everything you would have done with them in early D&D.
So modern D&D has the monster as natural animal (which reached its pinnacle in 2nd edition) and the monster as abstract combat challenge, a fighting algorithm, a sequence of attacks ticking away on a timer we call Hit Points. (Fixing the monster, in 4th edition, has mostly resolved around getting the timer to tick at the appropriate pace.)
What about the monster of the medieval bestiary? The bestiary too shares the D&D monster manual's concern with taxonomy. But what a different taxonomy it is! In the monster manual, the term "monster" eventually becomes a misnomer: "beast" would sometimes be better. In a great many cases, "animal," or "creature," would work just as well. The monster manual monster is not something that is wrong with the world. It is not something that does not belong here. It is not even something that is particularly unique or interesting, though there are plenty of wonderful examples where at least the D&D monster remains bizarre. But it remains something that we can classify, categorize, and taxonomize in a fairly naturalistic way. It can be explained. It has an ecological niche. It belongs in the world it inhabits. It is not symbolic. It does not carry a heavy handed moral, it does not stand in as a crude allegory for God or the Devil or sin or the sinner or redemption. It would not live long in a C.S. Lewis tale, and it would it live long in a medieval bestiary. The medieval beast is a creature of symbolism. In a bestiary, even a mundane animal, even a common, everyday, banal creature such as a mouse or an ant is something more. It is a symbol, a story, a little piece of Christianity and morality, of right and wrong, of spiritual warfare and the secret history of the world.
In the medieval bestiary, the even the most mundane of animals is made into a symbol. In the monster manual, even the most bizarre of monsters is made into a animal.