This article gives an execllent "big picture" summary of Nonprofits. It shows:
Rules for qualifying as a 501(c)(3)
Descriptions of other 501(c) sections.
It also talks about the situation where an entity incorporated as a nonprofit, does not seek federal exempt status.
Read the article by Community Enterprise Law,
Community Enterprise Law, a project of the Sustainable Economies Law Center (SELC), hopes to provide accessible legal information, best practices, and supporting tools for community-based enterprises and nonprofits.