The following is written for my home game that I am preparing right now.
Humans have created gods for a god to have power the god must be manifested and reified by the social body. The act of worship gives power to the god. Organized religion is essential for a God to exist. This is because for a God to exist there has to be enough worshipers and followers to manifest the deity. Rural areas often have petty gods because the local small scale worship of deities has less power to manifest a deity. Petty gods have become major gods over time when a rural deity has been brought into an urban population and spread with the birth of new religion reaching further parts of the world. Major gods have been known to begin as petty gods in rural areas.
Without memory, without worship, without a social body to reify and manifest a god it shall wither and die. Many times cults exist with the intended purpose of giving a chosen deity more power to move that deity from the place of being a petty god to the place of being a mighty God.
Demon gods exist in much the same manner as gods. Only demon gods come from alternate planes where the laws of physics differ. To gain power in this realm a demon God must gain worshipers. Much like petty gods, demon gods gain power as they gain followers and petty demon gods can become mighty Demon gods and vice versa. Because of the variations in the laws of physics between different realms the presence of a demon god brings chaos from the conflicting paradigms. The ways in which this can manifest differs greatly depending on the type of demon god, what the demon God is a god of and the various properties of the planes.
Rural religions, despite as much as they might try to hide it or show it otherwise, are very animistic in nature. You seek signs in the trees, in the grass, in the nature that surrounds you and is your everyday life.
Urban religions focus far more on ancestors, lineage, family, and patriarchy. This is because of the introduction of the concepts of property rights and inheritance that came with the removal from rural society. Religions do stress the importance of family ties, while rural religions do stress the importance of family ties, there is also a greater emphasis on community bonds and communal grazing. While both can be inherently oppressive they are such in differentiating ways. Both stress conformity and adherence to a patriarchal figure. While there is a patriarchal figure there is a communal approach in rural areas when decisions are made; for example while there is a male spokesperson for communal decisions they would be decided upon by the greater community.