The ponzi part of it is that current payers pay for current retirees. If the pension worked on a forced investment model where you paid into your own retirement and the money was invested for you that would be different. It would even be viable to say the money from those who died prematurely would be distributed to other users and it's possible to have the system generate more overall money for retirees than just what they put in and gain from investment.
However, the current system is quite far from that. The money you pay in goes nearly immediately to existing retirees with a moderate reserve of capital that is slowly decreasing as more money exits the system than enters it. This system cannot pay current retirees without the investment from new users, and that's what makes it a ponzi.
Pensions paid directly by current workers are not really so different from pensions paid out of investments. The thing that one "owns" in most of today's public equities is not physical capital (plants and equipment) but the "nexus of contracts" that allows you to make money from other peoples' labor. In other words, you are still living on backs of the working generation, same as Social Security or similar schemes.
Until we invent self-replicating physical capital (i.e. a Santa Claus machine that can make other Santa Claus machines), this will always be true.
All models are a ponzi that depend on a future generation doing labor. Retirement is ultimately a promise that someone will grow food and the other things you need/want. SS depends on the next generation being willing to pay, while stocks depend on the next generation willing to buy those stocks (or dividends because the company because the next generation bought things from it). Funds in a mattress depend on people wanting your cash.
No, they are not. “A ponzi” is a fraud. Some of the schemes you mention are not sustainable under certain hypotheses, but none of them have the deceptive and fraudulent aspects of Ponzi schemes, which is important. These are strategies, that might work out or that might not, but in any case they are not tools for personal enrichment through deception.
However, the current system is quite far from that. The money you pay in goes nearly immediately to existing retirees with a moderate reserve of capital that is slowly decreasing as more money exits the system than enters it. This system cannot pay current retirees without the investment from new users, and that's what makes it a ponzi.