You know the interesting story behind Ponzi-schemes, how Ponzi scammed hundred thousands of people selling stamps that did not exist. If not, Google it out after reading this short post.
So, the difference between MLM and the Ponzi pyramid model is that there is product behind MLM. And this product is basically such in nature, that customers order it because they need or want it, not because they are forced to. A huge difference. In the Ponzi model, usually a product does not even exist, or there is a product, but it's not beneficial for anyone.
Ponzi schemes are always scam, and they are illegal in most countries. They build on the naivety of people, who believe that they could be extremely wealthy. But in fact, they are forced to create a network and encourage more and more people to join and pay, till the pyramid collapses.
So we separate the two concepts by the value of product behind them.