Broadly speaking, these two words have the same meanings and can be used interchangeably in most settings.
一般来说，这两个词含义相同，在大多数情况下可以互换使用。
For example
他是我的哥哥。
He is my elder brother. ✔
He is my older brother. ✔
她是两个孩子中较大的一个。
She is the elder of the two. ✔
She is the older of the two. ✔
In cases like those above, elder is simply a more formal version of the word older, and when comparing two persons, elder has no implication of advanced age, just more advanced than its comparison. So, the elder brother in the first example isn t necessarily old in the sense of the later years of his life; he is just older than his comparison.
在以上的例子中，elder只是单词older的更正式的版本。需要注意的是，当比较两个人的时候，elder并没有高龄的含义，只是比它的比较对象更年长而已。所以，第一个例子中的哥哥并不一定是老年人，他只是比他的比较对象年长。
虽然这两个词可以用于表示相同的意思，
但在某些情况下，
根据句子的上下文，
你只能使用其中一个词。
For example
He is an elder member of the Supreme Court.
他是最高法院的资深法官。
The elder officer was honored by his younger counterparts.
那位年长的军官受到年轻军官的尊敬。
Elder表示较年长时，它含有对一个人的地位或成就尊重的情感。而使用older则没有这层含义。
The two words elder and eldest are used only when referring to people. They are not used when writing about animals or inanimate objects, such as clothing, furniture, etc.
elder和eldest只能用来指人。当描述动物或无生命的物体，如衣服、家具等时，不能用elder。
If the main point of your sentence is simply to showcase the fact of advanced age, then older is usually a better word choice.
如果这句话的主要目的只是为了显示年岁长这个事实，那么“older”这个词通常是更好的选择。
For example
The public opinion poll was a survey of older Americans.
这项民意调查是针对美国老年人的调查。
Older voters tend to show up at the polls more so than younger voters.
年长的选民比年轻的选民更倾向于参加投票。
Older can be used to refer to people, animals, objects, etc. There are no restrictions when using older to make comparisons.
Older可以用来指人、动物、物品等。使用older进行比较时没有限制。
older还有一种使用方式是不能与elder替换的
For example
Steve has an elder brother. (Correct)✔
John is the elder of the two. (Correct)✔
John is elder than Steve. (Wrong)✘
而older在这些形式中都是可以使用的
Steve has an older brother. (Correct)✔
John is the older of the two. (Correct)✔
John is older than Steve. (Correct)✔
总结，
因为这两个词大部分场合都是可以互相替换的，
所以你只需要记住他们每个词的限制即可
Elder只能用于人，
比older多了一份尊敬、敬重的感情
Older在绝大部分情境中都可以使用，可以用于人和物
与than连用时，只能是older than
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