There are 7 (+1 because of chimeras) classes of animals: Mammals, arthropods (insects, arachnids, myriapods, and crustaceans), molluscs (like slugs, squids and so on), avians (birds), reptiles, amphibians and fish - and chimeras that only live in Faizeon. Chimeras are basically just a combination of different classes of animals, like a mammal-avian or fish-reptile. They are natural creatures and were not artificially created. By the way, animals can still look monstrous even if they are not categorized as such. Something like a red four-legged creature that looks like a beast but is still a mammal is an animal. Monsters have specific types.
Plants of all kinds are grouped together into flora since there are too many different types to give each its own category. The specific type can be noted in their entries. (Disclaimer: I'm no biologist and I know there are probably more than 7 classes, this is to keep it simple.)
There are different groups of monsters: Golems, aberrations, imitators, slimes and plant monsters (there could be more if someone can come up with them). Monsters do not look like animals. Even if a creature looks like a big rat with way too big fangs, this would still be an animal and not a monster while humanoid looking creatures that are not Post-Eophrims are usually Non-Eophrims, so monsters are their own special thing. Not all monsters are aggressive and instantly try to kill people. A lot of them are, yes, but there are also those that are harmless or just want to protect their territory, just like it is the case with animals.