Is a Ponzi scheme considered a pyramid scheme?

One in the same. Ponzi scheme. pyramid scheme and now the Madoff scheme, all horses of the same color.
Madoff, of course makes Ponzi look like a petty criminal by comparison.

From Google search, for more clarity. Frankly I suspect that the first few levels of the original beginner in a pyramid scheme do make some money, but those at the bottom will never be the billionaire who is at the top. I have a sister who so believed in Amway, she stayed in for TWENTY years before she clued in. Meanwhile she and others have tried to drag me in but I want no part of MLM.

Multi-Level Marketing (MLM)
Legal multi-level marketing (MLM) involves being recruited in order to sell a product or service that actually has some inherent value. As a recruit, you can make a profit from the sales of the product or service, so you don't necessarily have to recruit more salespeople below you. And while you may be encouraged to recruit other salespeople whose sales would give you more profit, you can stick to just selling the product directly to the consumer if you choose.

A pyramid scheme MLM, however, will most likely sell a product with no independent value. The product could take the form of reports of some kind, for example, or mailing lists. In this kind of pyramid scheme, you would be required to recruit new members into the MLM in order to make a profit and keep the MLM alive. Joining the MLM is the only reason anyone would buy the products sold by this pyramid scheme.

Ponzi Schemes
Named after Charles Ponzi, who ran such a plot from 1919-1920, the Ponzi scheme is a fraudulent investment plan. It is not necessarily a pyramid, which is hierarchical. In a Ponzi scheme, there is one person who takes people's money as an "investment" and does not necessarily tell them how their returns will be generated. As such, the people's return on investment could be generated by anything; it could come from money taken from new investors - which means new investors essentially pay off the old investors - or even from money made by gambling in Las Vegas.

Actually, I must respectfully opine no, although they are quite similar.

In a pyramid, one person finds a few suckers, who each then get their own suckers, who get their own suckers, etc. So a person can come out ahead if, on balance, they do more suckering than being suckered.

In a Ponzi scheme, the pyramid is only one story tall. All the suckers are directly suckered by the Ponzi with no chance to do any suckering themselves.