The English language phrases Calm Down and Go Easy have related meanings, but they are different, as I shall explain, using British English examples.
Calm Down (verb) is an instruction to the listener to reduce their level of emotion.
"Calm down, children, we need to start the exercise."
"Sir, please calm down, or I will have to use the taser on you."
"Let's hope he calms down after such an exciting day."
"The water calmed down after the storm and we were able to set sail once again."
Go Easy (verb) is an instruction to the listener to be less severe in their actions.
"Please go easy around this next corner, it could be icy."
"Darling, please go easy on him, he didn't mean to break it."
"The guards went easy on the protester, they were secretly supporting his cause."
"Don't go easy on me, I want to know I am up to this challenge."
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