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I have to explain the difference between slim and skinny to an elementary student with little grasp on the English language.

Slim is a more positive word. It means healthy and when you touch the person you can feel muscle. Skinny is very boney so when you touch the person you feel bones.

Does this even come close to a decent explanation to a young child?
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Correct. You might add, however, that "skinny" is often used to make fun of people, not just a less positive word.