plan：The word "plan" is typically most used to describe making a plan to do something/anything.

"plan"这个词通常最常用来描述为做某事或任何事情而制定的计划。

Do you have any plans this weekend?这个周末你有什么计划吗？I didn't plan to visit you today, but since I was nearby, I did.我本来不打算今天去看你，但因为我在附近，所以去了。

scheme：A "scheme" is much more detailed and large-scaled than a "plan".

一个 "scheme"比一个"plan"详细得多，规模也大得多。

The gov. launched a scheme for the people's welfare, I'm planning to go travelling during these vacations.州长发起了一项人民福利计划，我打算在假期旅行。The word "scheme" however, is less used for casual planning and more so to describe making a plan to do something ilegal or wrongfully like theft, bank robberies, pranks, and other negative tasks. It could also be used to describe planning something devious. But a plan is neutral.

然而"scheme"这个词不太用于随意的计划，更多的是用来描述计划做一些不合法或错误的事情，比如偷窃、银行抢劫、恶作剧和其他消极的任务。它也可以用来描述计划一些诡计（计谋）。而一个"plan"是中立的。

Whatever scheme you came up with, forget about it.不管你想出什么谋划，都别提了。Was this all a scheme to get me out of the house, so you could plan my surprise party?这是不是一个让我走出家门的计谋，这样你就可以安排我的惊喜派对了？”