Before his fall from grace, Lucifer was the highest of God's Angels. As a result of his pride and through his own free will, he displeased God greatly. This resulted in his eternal damnation. The Devil's job is to test the faith of the people created by God; to tempt them into committing sinful acts. For example, he helped Eve choose to eat the forbidden fruit, which led to Adam and Eve's expulsion form the Paradise.
The writings St. Thomas Aquinas are useful in better understanding the Devil's place in the Judeo-Christian God's creation, especially as he relates to Christians. Aquinas is one of the most significant mediaeval theologians. His writings form the basis for most of Christian thought. He wrote, in his Summary of Theology that Evil is the result of privation or unnatural lack of God's 'Goodness'. The magnitude of evil corresponds to the amount of missing goodness in a creature or event, in relation to the magnitude of its total potential goodness. For example, most birds have wings and can fly. This ability of flight is good. It is available to birds because they were created by God, through His goodness. Should a bird have a broken wing, it lacks the ability to fly. This is an example of a minor evil: the lack of a 'goodness' that it should possess. The Devil started out as the highest of the angels. He has the potential for the greatest goodness in creation, second only to God Himself. After his fall from grace, he now lacks all goodness and represents the greatest evil in all of Creation. This is because he has (had) the potential for the most goodness.
The 'Horned God' and the 'God of the Underworld' are not 'Angels who have fallen from Grace'. Their stories are completely different from that of the Judeo-Christian Devil. Although the behavior of some of these Deities is not always 'nice', their role is not to tempt mortals into doing sinful acts and testing their faith. They do not exist to lead mortals away from proper worship of the single creator God. The Judeo-Christian 'Hell' is also not the same as the Greco-Roman 'Underworld'.
The horns of the 'Horned God' are an allusion to the antlers of a Stag, not the pointy horns seen in traditional illustration of Satan. Pre-Christian European cultures had a deep reverence for Nature. The Stag or male deer is a graceful, yet powerful animal. This natural beauty is the inspiration for the horns of their God, who represents all that is masculine.
The God of the Underworld, known to the Greeks as Hades, is one of Zeus' two beloved brothers. Zeus did not create him. He is made lord of the underworld, ruling over all the dead. Like the Devil, He is a greedy god who is concerned with increasing his subjects. Unlike the Devil, Hades receives all those who die, not just the sinners. For this reason, he has no need or reason to cause mortals to commit sinful actions. He may be unpitying and terrible, but He not capricious or evil. Unlike the Devil, He has a wife, Persephone who lives with Him half the year. Note also that He is the King of all the dead but, death itself is another god, Thanatos.
Unlike in the Judeo-Christian Hell, life in the underworld is not a place of fire and brimstone. It is rather like a miserable dream, full of shadows, without sunlight or hope. It is a joyless place where the dead slowly fade into nothingness. It is not a place of eternal pain, torment and torture and punishment as Hell is often said to be. Unlike Hell, Hades' underworld is for everyone, not just sinners