I think my terminology might not be the test (non-english native speaker).
When I say initial offering, I mean whenever stock is newly (initially) issued - whether that's in IPO, after an IPO or also in a private offering. Not sure what the correct term would be.
My point was, money essentially only flows into the company at that point.
E.g. company issues stock, investor A buys it.
When investor A sells to investor B, money only flows between these two investors. No money flows to the company.
Unless - as you have pointed out - company assumes the role of an investor in its own stock.
But the fact alone that a stock price is rising as such does not generate any new capital to work with for the company. And that is a point many people seem to misunderstand.
When Microsoft is worth 3.76 trillion USD, that doesn't mean that Microsoft has 3.76 trillion USD it can work with. That was the point I was trying to make.
That's true but saying that investors moving money between each other is a "pretty accurate description of how the stock market works" is simply incorrect.
The above is a mere byproduct of the market working. The market "works" by giving companies and entrepreneurs access to capital, the rest is a derivative of that. Otherwise you can as well trade postal stamps rather than stocks.
It wouldn't be called "Initial Public Offering" if it was the "Only Public Offering" like you suggest.