I have long puzzled over the question of which is correct - "derivative suit" or "derivative action"? Historically, the term "suit" was used for proceedings in equity. California courts have generally regarded shareholder derivative claims as equitable. Nelson v. Anderson, 72 Cal. App. 4th 111, 127, 84 Cal. Rptr. 2d 753, 763 (1999). Thus, one might conclude that the proper term is "derivative suit".
Yet, one can find many examples of California courts referring to "derivative actions". See, e.g., Grosset v. Wenaas, 42 Cal. 4th 1100, 1103, 175 P.3d 1184, 1187, 72 Cal. Rptr. 3d 129, 132 (2008) and Small v. Fritz Companies, Inc., 30 Cal. 4th 167, 185, 65 P.3d 1255, 1266, 132 Cal. Rptr. 2d 490, 503 (2003). Perhaps even more odd is the fact that the Delaware Court of Chancery, which is a court of equity, refers to stockholder derivative actions. Del. Ct. Ch. Rule 23.1.
One might look to the California Corporations Code for guidance. Surprisingly, however, the General Corporation Law never uses either term. Section 800(b) refers somewhat verbosely to an action "instituted or maintained in right of any domestic or foreign corporation by any holder of shares . . .". The term "derivative action" does appear in several sections of the Uniform Limited Partnership Act of 2008. See, e.g., Cal. Corp. Code § 15910.05. The more recently enacted Social Purpose Corporation Act uses the chimera term "derivative lawsuit". See, e.g., Cal. Corp. Code § 2900(b).
All of this leads me to conclude that authority can be found for using "derivative suit", "derivative action" and even "derivative lawsuit".