'Scheme' in this case is a Britishism, basically meaning a project (not something nefarious).
Scheme itself means the same thing but it's fallen out of use and the only times I've encountered it is when the speaker wants to distance themself from it: get rich quick scheme, hare-brained scheme, nefarious scheme, malicious scheme, etc.
I note we here use schema, which is partly why I interpret a scheme neutrally.
I don't know how the word carries so substantially different moral leanings, but that's English. I'm sure there are many other words with evil twins.
There's a book published by some Brits in Oxford that very usefully researches the history of English words. They have found examples of all the meanings discussed here from the mid-to-late 17th and early 18th centuries, FWIW.