Plan is the will and intention to carry out some action. while Scheme is an elaborate and systematic plan of action. cowboy...

Plan means to make the intention to do something. Like "I plan to pay the phone bill." Scheme means an elaborate plan. Like "Ron started to scheme a plan that would ultimately enslave the world."

And "scheme" is usually used in a negative sense, when someone is trying to trick people, steal from them, or something else like that.