I guess the question could also be, is 其他 any different from 别的?
Is one any more formal, any more slang, any more rude, anything of the sort, than the other?
Or are they essentially the same?
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They are similar in the meaning, however, not exactly the same.
其他 has a meaning of "the others", but it also has the meaning of "the rest", since this word is often used in the last when you are listing some categories, for example, "这个项目, 小王负责写代码, 小李负责 code review, 其他人去做测试." this word has the meaning in dividing the scopes.
别的 also has the meaning of "the others", for example, "我只知道这些, 别的我不知道了", in this sentence, the speaker tries to emphasize what he knows ("我只知道这些"), since "别的", from the literature meaning, "别"+"的", 别 has the meaning of different, so this word has the tendency in comparing and emphasis.
No difference in meaning at all.
A good way to think of 其他人 may be "The rest of people" or "The rest of individuals". 别的人 should be translated as "other people", which is not grammatically wrong, but it does sounds unnecessary when you can just say 别人.
EX: Here is an example where it is acceptable to use either. 我已经开始着手解决这件事了, 其他人就不要再插手了. 我已经开始着手解决这件事了, 别人就不要再插手了.
First of all, “别的人” isn't used quite often,at least not used often by Beijingers, more common form is "别人"
“其他人” always represent the rest in a team, class, squad, etc. It's more formal, and more specific, and when you want to explicitly refer to some people, use this word, especially when you are assigning works to people. You can still use "别的人" or "别人" if you wish, but not if you're writing a news report, research paper, etc.
"别人" has the same meaning. But it's informal. When you're chatting with someone, use this word. Again, you're still allowed to use "其他人".