In some context they are synonyms to each other.
Conspiracy= a secret plan by a group to do something unlawful or harmful:
Ex- a conspiracy to destroy the government
[mass noun] the action of plotting or conspiring: they were cleared of conspiracy to pervert the course of justice.
Scheme :a clever and often dishonest plan to do or get something
Ex-a scheme to cheat people out of their money.
plot: a secret plan to do something that is usually illegal or harmful .
Ex. plots against the government .