The only time we use 'elder' is for family members, as an adjective placed before the noun. For example, you might say 'my elder brother' or 'my elder daughter'. In all other situations, we use 'older' - for example, "My brother is older than I am". In fact, you don't need to use 'elder' at all. It's OK to say either 'my elder sister' or 'my older sister'. Both are correct and there's no difference between them. I'm a great believer in keeping things simple for students, and forgetting about words that you don't need to use. Just as with while/whilst, any more/anymore, and (more controversially) further/farther, you can often manage fine by always using just ONE of the words in a confusing pair. My advice would be to forget about 'elder'.

I always say that you can use both older and elder to describe nouns (so not just people), but elder is usually used for family members or relations. I can't think of any times I have heard or used elder people. Older people does not have to mean the elderly - you could talk about classmates or colleagues at work and use older people, so yes to the use of older people not meaning the same as the elderly. Hope this helps :-)