In context|mathematics|lang=en terms the difference between system and scheme

 is that system is (mathematics) a set of equations involving the same , which are to be solved simultaneously while scheme is (mathematics) a type of topological space.

As nouns the difference between system and scheme

 is that system is a collection of organized things; as in a solar system while scheme is a systematic plan of future action. 

As a verb scheme is

 to plot, or contrive a plan.