Elder is used in 2 cases:
when talking about family members: ex. Peter is my elder brother.
it is a more polite word for all people of a certain age. For example you can say : This hospital is for old people, but a more polite way would be: This hospital is for elder people.
The word "older" is an adjective , the comparative form of "old".
The word "elder" is an adjective and a noun :
- the adjective "elder" describes a noun as one or more of a group that is of greater age;
- the noun "elder" is a word for someone of greater age than another; a type of church official; a type of tree,
I have an older model telephone with a cord connecting the receiver,
Which of your daughters is older ?
This is my elder daughter, Susan. (adjective)
Susan is the elder of my two daughters, (noun)