Barnaby Zall (Of Counsel, Williams & Jensen, P.C.) provided a useful summary of key sections of the IRC to the CyberAccountability email list:
Section 170 - recognizes non-profit status, but not exemption from federal taxation.
Section 501(c)(3) - recognizes that some non-profits are exempt from federal taxation.
Section 509 - recognizes that some 501(c)(3)s tax-exempt non-profits are also exempt from private foundation rules - i.e., all 501(c)(3)s are private foundations unless exempted under Section 509.
You can be a 501(c)(3) charity without being a private foundation, but you must satisfy either a public support test, a source of income test, or a supporting organization test, under Sections 509(a)(1), (2) or (3).
When you apply for (c)(3) status, you receive both a tax exemption and a ruling on your private foundation status under section 509. If you are not considered a private foundation, your original status under Section 509 is temporary, and must be renewed within a few years by showing that you actually do meet the requirements of Section 509.
"Public foundation" is a phrase I have heard before, but it's not common. The technical term is "not-a-private foundation," and I wish we had a better one.
Barnaby Zall Of Counsel Williams & Jensen, P.C. Washington, D.C. (202) 659-8201