Initially, there was very little difference. In general, every higher power among the deities of the Olympic Pantheon and human beings were considered a "demon." In and of themselves, they were neutral, which is to say they could be good or evil. They correctly guided men using reason (the demon that Socrates was believed to have had within him) and telling him what to do, which sometimes led man to destruction (i.e., falling into misfortune or illness). This duality represents, as it does in other religions, the ambivalence that humans felt regarding their relationship with the gods.
Think about Hephaestus (known as Vulcano to the Romans), for example. He had a terrifying nature. There's a dichotomy at play in this god. He was the god of industry and metalworking, but, he was also the force behind volcanoes, which were destructive and unconquerable; not only that, he was also associated with dens, caves, and mountains. Consider also Aphrodite, the goddess of sensual love, who was sometimes the cause of the wildest forms of folly–pernicious and disgraceful acts.
The origin of other evil forces is also similar to what we find in the Mesopotamian region and perhaps influenced by it. Here's a brief summary of one story worth considering. Initially Chaos begets Uranus (Heaven) and Gaia/Gea (Earth). Over an indeterminate period of time, these two lay in a perpetual embrace. They have offspring naturally, but in such a way that it feels compressed and overwhelmed, continuously within the bosom of Mother Earth, engaged sexually without any rest by Heaven.
Gaia decides to free herself and her children from this continued oppression. She forms a sickle and gives it to one of her sons, Chronos (Time), who attacks his father and castrates him. With this action there comes an end to the continuous sexual embrace between Uranus and Earth, and both can be separated. This begins the life of the universe. Chaos, once he fulfilled his primary mission, withdraws from the scene to a state of solitude and almost perpetual isolation. Blood from the genitals of Uranus bore twelve monstrous beings, the Titans, who were divine but inferior beings that harbored a deep hatred for the rest of the gods from the moment they were born.
Chronos joins one of his sisters, Rhea, and give birth to a number of children. They are, as in Mesopotamia, young gods, knowns as the Olympians. These are destined to succeed the old primordial gods. But just as Uranus, with his continuous sexual activity, did not let his children escape from the womb of Gaia, Chronos devours his own children one by one.
Rhea feels enormous grief and concocts a scheme to save her beloved son, Zeus, who was also going to be devoured. Instead of swallowing him up, Chronos swallowed a rock, and was thus deceived by his wife. Zeus then comes out of hiding and kills his father. This action angered the Titans, the brothers of Chronos, who are ready to avenge Zeus. But they are beaten and chained by him in the underworld. From there, envious, disgruntled and embittered by their defeat, they try to send forth all the evil that they can. Because of that they soon become identified with Evil itself.
Another monster, Typhon, jumped into the fight as an ally of the Titans. He was created by Gaia, the consort of Uranus, to take revenge on Zeus because of what he did to the the Titans. Typhoon lives underground and his body, from the hips down, is made up of two terrible snakes, while his shoulders have a number of other frightening reptiles. Typhoon mates with her Echidna and has countless other evil monsters, including Hydra and Cerberus, the guardian of the gates of Hades, which is Hell.
Thus, with good gods and a certain need created by primordial chaos, all of this gives rise to evil deities, which, over time, eventually become demons. Everything happens it seems because the universe of gods and men needs both a good part and a bad part, as if good and evil could not exist one without the other.
Greek mythology had another series of evil gods, lesser deities, which perfectly fit into the category of malicious demons. These include:
1. The Ceres, often cranky spirits, who had terrible claws and terrible faces, whose mouth was always hungry for the blood of the dead.
2. The Lamia, like the Mesopotamian Lilitu, which sought the death of infants in the night.
3. The Harpies, female monsters in the form of birds with human faces, who fly around robbing mortals.
4. The three Gorgons (the most terrible of whom was the Medusa), demons of the sea and shipwrecks.
5. The Hydra, huge serpents with multiple arms.
6. The Furies, spirits who took vengeance on criminals.Apart from cosmological myths and within the religious world in the broadest sense , we find two lines of thought that influenced the pre-Christian era in the development of conceptions about demons: Orphism and Platonism.