Both are comparative form of the adjective ‘old’. You can say:
Old….. older …..oldest
old ……elder……. eldest.
Both imply having greater age than something or someone else. While ‘older’ finds common use, Elder, has restricted application and is used chiefly to indicate seniority in age as between any two people but especially priority of birth as between children born of the same parents:
The elder brother became a minister.
He is an elder statesman enjoying considerable respect.
There is tax incentives for elder citizen in India.
You can also use elderly as a polite or respectable word for the ‘old’ people.
He visits his elderly parents very often.