Regarding the creature types, Monstrosity and Beast.
A Beast is − or is comparable to − a reallife animal.
The result of splicing different animals together, such as by genetic engineering, is still an animal.
A duckbill platypus, or a newly spliced amalgum of different animals, or a Star Wars scifi animal physiology that "might" have evolved, are all Beasts.
A monster is something different.
A monster is mythic. It is dreamlike − typically nightmarish − with an ominous presence that psychologically connects and haunts its viewers. Somewhat like a ghost, a monster has a psychologically compelling aura of magic around it. One expects a monster to do things that are impossible to a natural animal.
A Dragon is a specific kind of Monstrosity. The dragon derives from Greek stories about the "drako", namely the python in Africa, but evolves in the collective storytelling and artistic reconstructions of what it looks like, which often blends the image of the "draco" Roman tubular military banner with various animal heads. By the Medieval Period, the classic dragon splices together snake-eagle-lion. The British dragon seems to be moreso snake-wolf-bat. If this is all it would be, a strange-looking animal, then it would be a Beast. But the Dragon has a nightmarish aura of magic. It is especially a manifestation of primal dangers and fear instincts. Fear of fire, fear of predatory animals, fear of poisonous snakes, and similar. A Dragon is a manifest nightmare with a psychologically haunting quality and influence. The Dragon is especially distinctive because similar snake-splicings with a haunting quality seem to show up across many human cultures. Because of the special characteristics, D&D separates it out from other Monstrosities, to give it its own creature type. Even so, the Dragon is a good example of the difference between a Monstrosity and Beast.
A Monstrosity doesnt just look scary, it is a magical manifestation of the fear itself. The monster is even moreso a dream inside the head of the viewer. Rather than a creature outside, over there. A ghost has a similar mythic quality. One expects a Monstrosity to do magical things that would be impossible for a natural Beast.