Hi, Tam.
That depends. If you are using "elder" as an adjective, then it means the same as "older":
- I have an older brother
- I have an elder brother
Except "elder" is relatively more traditional, perhaps formal.
However, if you use "elder" as a noun, it no longer means "older". It means an aged person:
- The elders in my village have gathered for the annual Council.
By that you mean those oldest in age have gathered. You CANNOT say "the olders in my village".
LIkewise, "old" and "elderly" are similar, but there are contexts in which they are not interchangeable. For example, you can use both as an adjective to define people; but you can't use both for inanimate objects, and you cannot use "old" by itself in a sentence, given that it acts solely as an adjective. For example:
- The book is old. (You cannot say "the book is enderly")
- Worry made him old. (You cannot say "elderly").
To use "elderly" you would have to change your sentence:
- Worry has made him an elderly man in my eyes.
Also:
- The elderly in my village are so wise. (You cannot say "the old in my village")
If you want to use "old" in the previous sentence, you would have to use a noun after the adjective:
- The old *people* in my village are so wise
Though you can also use "enderly" as a pure adjective:
- The elderly *people* in my village are so wise.
And you can't use "elderly" for things:
- This is a 50-year old rock (not "elderly")