I’ve read both forms in newspapers and online news: elder brother and older brother.
What’s the difference between them? When should I use which?
They are both essentially the same and are for the most part interchangeable and no one would notice or correct you. That said, ‘elder’ will typically sound a little more formal than ‘older’
In typical usage, I personally would say “My/his/her/their older brother” when speaking of a specific person’s sibling. I would say “The elder brother/sister/sibling” to refer to the oldest of a group of siblings. I suppose that also brings out another point: I would typically use
elder only when referring to the oldest of the group (I would not say “his elder brother” to refer to the the second-born from a set of three siblings, where ‘his’ refers to the third-born).
That said, they are almost completely interchangeable and at worst will lead to mild confusion as to which older/elder person is being referred to when there are multiple choices.