Either of them has a pen.Both of them have a pen.

Question

意义上的区别在哪？

Answer 1

本质意义上是没有区别，但是具体描述上有区别：
Either of them has a pen. 他们两个人中的任意一个人有一支笔
Both of them have a pen. 他们两个人都有一支笔
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Answer 2

OK