The Pyramid scheme

A pyramid scheme is a form of fraud similar in some ways to a Ponzi scheme, relying as it does on a mistaken belief in a nonexistent financial reality, including the hope of an extremely high rate of return. However, several characteristics distinguish these schemes from Ponzi schemes:

In a Ponzi scheme, the schemer acts as a "hub" for the victims, interacting with all of them directly. In a pyramid scheme, those who recruit additional participants benefit directly. (In fact, failure to recruit typically means no investment return.)

A Ponzi scheme claims to rely on some esoteric investment approach (insider connections, etc.) and often attracts well-to-do investors; whereas pyramid schemes explicitly claim that new money will be the source of payout for the initial investments.

A pyramid scheme is bound to collapse much faster because it requires exponential increases in participants to sustain it. By contrast, Ponzi schemes can survive simply by persuading most existing participants to "reinvest" their money, with a relatively small number of new participants.

A bubble: A bubble is similar to a Ponzi scheme in that one participant gets paid by contributions from a subsequent participant (until inevitable collapse), but it is not the same as a Ponzi scheme. A bubble involves ever-rising prices in an open market (for example stock, housing, or tulip bulbs) where prices rise because buyers bid more because prices are rising. Bubbles are often said to be based on the "greater fool" theory. As with the Ponzi scheme, the price exceeds the intrinisic value of the item, but unlike the Ponzi scheme, there is no person misrepresenting the intrinisic value; investors typically know they are in a bubble.

"Robbing Peter to pay Paul": When debts are due and the money to pay them is lacking, whether because of bad luck or deliberate theft, debtors often make their payments by borrowing or stealing from other investors they have. It does not follow that this is a Ponzi scheme, because from the basic facts set out there is no indication that the lenders were promised unrealistically high rates of return via claims of unusual financial investments. Nor (from these basic facts) is there any indication that the borrower (banker) is progressively increasing the amount of borrowing ("investing") to cover payments to initial investors.