California's new female director quota requirement applies to publicly held domestic or foreign corporations with their principal executive offices located in California.  Cal. Corp. Code §§ 301.3 & 2115.5.  California's older Public Disclosure Act requires publicly traded corporations and publicly traded foreign corporations to file an annual disclosure statements with the California Secretary of State.  Cal. Corp. Code §§ 1502.1 & 2117.1.  The terms "publicly held corporation" and "publicly traded corporation" are easy to conflate, but there are at least two key differences.  

A publicly held corporation is defined as "a corporation with outstanding shares listed on a major United States stock exchange".  A publicly traded corporation is defined as a corporation or foreign corporation that "is an issuer as defined in Section 3 of the Securities Exchange Act of 1934, as amended (15 U.S.C. Sec. 78c), and has at least one class of securities listed or admitted for trading on a national securities exchange, on the OTC Bulletin Board, or on the electronic service operated by Pink OTC Markets Inc.".  

The first significant difference between these definitions is that a publicly held corporations must have shares as opposed to securities listed on a major United States stock exchange.  Thus, publicly traded corporations include corporations that only have debt that is traded in a specified market.  A second difference is that a publicly held corporation's shares must be listed on a "major United States stock exchange" while a publicly traded corporation's securities must be listed or admitted for trading on a "national securities exchange" or specified on a over-the-counter market.  The legislature has not defined "major United States stock exchange" but presumably the New York and Nasdaq stock exchange qualify.  According to the Securities and Exchange Commission, a "national securities exchange" is a securities exchange that has registered with the SEC under Section 6 of the Securities Exchange Act of 1934.  The SEC currently lists more than 20 national securities exchanges, including the NYSE and Nadaq exchanges.  (For more on national securities exchanges, see this blog post from 2011).

These differences are significant because it is important to understand that not every corporation filing a disclosure statement is a "publicly held corporation" even though it is a publicly traded corporation.