In Greek mythology, creatures are born one of three main ways. Two ways include gods having children with other beings. Firstly, A god can have a child with a spirit, usually one involved with an element, the result is usually a mythological creature or a lesser god. Then a god can have a child with a mortal princess/queen, and the resulting offspring is either a half-blood champion or a monster. Then there is the classic child of Echidna the mother of monsters, who is actually called that in myth and is understandably the mother of most of the normal Greek monsters.
Norse mythology is likewise convoluted in how its creatures are made. There are a lot more unions between gods and other races that result in more animalistic children. These include but are not limited to Sleipnir Lokis spawn, Jormungandr Lokis spawn, and Fenrir Lokis spawn.
With the classification of monster comes a need for a way to define both humans and other sentient races in mythology. Some mythologies take a human first approach and label anything other than human a monster, such as Greek Myth. Or they develop their meaning for monster some, like Norse myth, which allows for the existence of giants and dwarves, and other creatures not immediately labeled monster.
These humanesque races of people are so close to human but differ in small ways. Most near-human beings are seen as having extraordinary powers. From myth to modern D&D, fiction has heavily leaned into these stereotypical views on inhuman people. Elves are seen to be graceful and long-lived, but the reality is that people that eat vegetables and take care of their body are more likely to live longer than those that don't, pointed ears aside. Giants and Dwarves are two sides of the same coin, that coin being the difference in size. Most real life giants are seen to be physically stronger, though that is also scientifically possible due to the physical ability to have more muscle mass that comes with having longer and larger limbs. Dwarves are seen in fiction as being portly, though if the vertical height of a person were reduced they would indeed seem physically stockier, just how some taller people seem gaunt in comparison.
Monsters are largely a matter of perspective. If monsters have a basis in fact, then the feeling associated with the basis is carried over to the fantastical. Most monsters fall under some common groupings, such as; animals, fears/nightmares, and historical. Animal monsters include any larger than life monster which has a corresponding animal basis. Famous ones include the Nemean Lion, Jormungandr, and the Erymanthian Boar. Other than physical size, these monsters could have quirks such impenetrable skin or a means of paralyzing their "victims".
Monsters that fall under fears and nightmares are based on common fears of humans, ranging from charybdis which personifies the fear of whirlpools to the Bogeyman which was used to frighten kids who disobeyed their parents. These monsters are born from the fear in a persons own mind, and are uniquely feared by certain people.
Historical monsters are those that have a realistic or semi-realistic basis in history. This includes Vampires, Mummies, and Witches. These monsters have either a singular basis, like how the Vampire myth is centered around Vlad (Tepes) III, Prince of Wallachia, or multiple bases such as mummies and witches. In the case of mummies and witches, they were not initially feared by the people of the time, Witches were even part of medicine and religion in pagan societies. The fear was cultivated by superstition and grew among uneducated masses.
Medusa- Cursed by Athena, due to Poseidon
Minotaur- Monster, mother was cursed to fall in love with a bull
King Lycaon - cursed after feeding his children to the gods in a stew, first werewolf.
