Hello Bel!
They are synonyms and elder sounds more formal than older.
Older indicate someone or something more aged than another one. For example: David is older than me / This chair is older than that one.
Elder has the same meaning of older (comparative) but you can use it only talking about human beings and mostly in family relationships; you can't add "than" like after older. For example: Lisa is my elder sister (otherwise would be: my sister Lisa is older than me).
Furthermore, elder can indicate someone of higher rank, such as a corporal or a manager.
In everyday speech older is widely used, rather than elder.
Hope I have clarified!
All the best,
Noemi