Many people -- see investopedia and wikopedia and, I can tell you, at least some Wall Street corporate lawyers, use "secondary" offering to mean any offering after the "initial" public offering.
Many people spell “lose” as “loose,” but that doesn’t make it right.
I challenge you to find an actual SEC filing in which the term secondary offering is used in the manner described in Wikipedia rather than in the correct manner of meaning a sale of shares by a party other than the company itself.
“The efficient-market hypothesis may be the foremost piece of B.S. ever promulgated in any area of human knowledge!”