I mean I'm asking, how are they actually different, besides one being worse for the shareholders w.r.t. taxes? They both involve transferring $X to shareholders.

Dividends are also saying "we have this amount of money on hand or cash flow, and no better use for it, so here you go"

I don't see the difference. Stock buyback looks to me like dividends without the tax - imagine a dividend reinvestment plan without the middle step and the tax bill.