"別”＝different "他”=other I'm going with someone else = 他の人と行くことになってるんです。 and 別の人と行くことになってるんです。you can use both　他　and 　別. ("他の人と行くことになっています” means "他の人と行きます”.but you have to say "他の人と行くことになっています。this is close to " I'm sorry I'm going with someone else".Of course you can say "申し訳ありませんが、他の人と行くことになっています。” ”他の人” isn't ”他人”.　”別の人”isn't ”別人”

In that case, I would use 他. I'm going with someone else = 他の人と行きます/行くんです (I will add a better explanation of the difference between 他 and 別 if I could find or think of any, now I got confused too.. ごめんなさい)

In my opinion,他 means he. 别means the other person. if you want say "please give the book to him",you can say 请把书给他。他is concered above,we all know who is he.But if you want to say"give the book to anybody else" 把书随便给其他人吧。别人means anybody else.Both of them can be used as noun word. In some situation,别人和他人can exchange

I was a bit confused at first, cos "他" and "别" have totally different meanings. I guess what you mean "他人" vs "别人". :) In the case you mentioned above, you should use "别人".