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Is "to stay in touch" correct? Is that used by native English speakers? Or is there any difference between the two idioms? Thank you ver ymuch.
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I'm not a teacher here, but I'd say
"let's stay in touch" with someone you've already been in touch with: "let's go on being in touch"
"let's keep in touch" either with a new topic, or with someone you've just met and want to be in touch with.
Emotion: smile
Comments  
I believe they are both correct.