Well, no, not really. You're relying on the fact that you own some assets, which you can sell to someone else who wants to own those assets. That's very much not "ponzi-like".
This is counterintuitive, but globally saving is not possible, in a financial sense. IIRC from economic models it nets out to investment.
Which makes sense. Real world saving is amassing a grain store, or an oil stockpile in a strategic reserve, etc
And we can't do very much of that. Monetary savings depends on the ability to buy things of value from a later generation of producers.
A small country can use savings to buy from other countries. The larger the country, the less possible that is, as the large country becomes a significant portion of the world economy.
A simpler way of looking at it is: if the future generation started producing half as much, you wouldn't expect monetary savings to command the same worth in terms of real goods that they used to.
Of course, generally you wouldn't exchange your assets directly for food or healthcare; more likely you'd have stocks and bonds and make money from some combination of selling on to non-retirees and taking some of the profits when they buy things from those companies, but it's ultimately what you're doing in the end.
Retirement is non-ponzi like because the assets appreciate in value due to increased predicted future earnings. This is totally different from paying out what others pay in.
Assets can appreciate in value and income even without new investment.
You can trade those for things, now. In saving for retirement, you're planning to trade the earnings from those assets for future things made by future workers.
Assuming the economy continues relatively normally, we'll be able to do that when we retire. (I don't think retirement is a ponzi scheme).
But, I do think it's worth considering things from that angle. For example, could everyone do FIRE (financial independence, early retirement)? No. At least, not unless in their efforts they created perpetually working robots to replace everyone who retired.
To put this in other terms, you could say I'm saying "if there aren't enough future workers, the future value of investments will decline, causing retirement shortfalls". Which, again, doesn't make retirement a ponzie scheme. I'm just providing another frame: money can be confusing. It doesn't work in the aggregate the way it does for an individual.
Saving money is an illusion. The government can't just put your pension contributions into a savings account and withdraw it decades in the future. It must use the contributions of current workers to pay the pensions of current retirees.
Food doesn't last forever. If you buy food in your 40s the food is no longer edible in your 60s. If you don't buy food and instead choose to save your money the food is still going to rot away. You now have money but no food. As a retiree you are dependent on the current working generation to work for your food.
It doesn't change the fact that your second paragraph is true though - just a nitpick.
It doesn't make any of it like a ponzi scheme.
Exactly. The corn you eat needs to be grown today.
Fundamentally, I think there might be a deeper issue at play here. There's a common (and dubious) argument that Social Security is a ponzi scheme because the payments to retirees come from funds contributed by new investors. On some level, though, all of retirement is a little ponzi-like; ultimately you're always relying on the current working population to pay for your retirement, no matter what investments you put into your pension fund. What happens if that goes pop?