I am not the one that is confused.
You asked me what the difference in cash flow was, and I described it. A pension fund is actually legally required to follow the laws about having enough assets on hand to cover their obligations, SS does not.
That's not true. Most places don't have laws which say that pension funds have to be fully funded. In fact, most aren't. Pension funds are bounded by laws in which they are supposed to operate. But they don't have laws that say "You have to have $X in assets to pay $Y in liabilities."
I have no idea why you are so hung up on the bond buying part of this. The point is that the pension fund does not transfer payments from current workers to current retirees, SS does. That is the significant part of the cash flow in this discussion, not the bonds. SS relieas on the transfer payments, not the bonds, to meet its obligations. Pension funds do the opposite.
I am hung up on the bond buying part because a pension plan comprised entirely of government bonds
does transfer payments from one set of workers to another. In fact, all government debt - or all debt for that matter - transfers assets from one group of people to another.
I'll give you an example. Lots of people say that "The SS trusts are just filled with IOUs." Never mind that all bonds and debts are merely IOUs with different legal standings, that doesn't change the economics and cash flows of the funds. Let's say I borrow money from you. We can do it two ways. I can promise to pay you back (an IOU) or we can write a contract saying I will pay you back (a bond). Then I pay you back. Between the time when I've borrowed money from you and the time I've paid you back, in the first scenario, you have my promise, the second, you have a bond. That doesn't change the cash flows and economics of the transaction. The only difference is the legal standing of the asset and liability and perhaps the liquidity.
I get why this is confusing, but if you drill into the economics, the cash flows are all the same. The government could set up an individual mutual fund administered by a private company for every one on social security which can only invest in government bonds, and the economics and cash flows would be exactly as they are in the SS trusts.