A scam is illegal. A scheme is not. A scheme is not necessarily a scam. Scam scheme or scheme scam is a bit redundant, but is still correct if you are speaking of **other types** of schemes or scams in the same writing. If solely speaking of scams that are schemes and vice versa, do not use the two words next to each other. Doing so would be redundant (I am redundant here for clarification to ESL readers). **Redundant/redundancy is saying the same thing twice immediately when it is obvious they have the same meaning.**

Scheme is a somewhat neutral word, although slightly pejorative.A scam is a scheme to cheat someone.

A scheme is a system or arrangement, while a scam is something fraudulent or dishonest intended to trick and deceive. A Ponzi scheme is a scheme and a scam because it's a systematic scam. Hopefully that helps a bit.

It's just by convention. A "ponzi scheme" is a scam. scheme - a plan, good or bad scam - a plan to trick people. by convention, we always say "ponzi scheme". that's just the term. but gramatically speaking, "ponzi scam" does make sense. it would just sound strange, because we do not say it this way.