What I've learned is Japanese refer to their family differently than they would refer to other peoples family. Like 'Haha' being mother, but also 'Okasan' is mother. However, everything I've seen in anime and manga they always refer to their family members using these titles like Otousan, One-chan and so on. Is this one of those instances where you can't trust the manga/anime?
Talking about your mother to other people, you say 母 'haha'. That is an exceptionally weird thing to call her to her face, though; in that case, you say お母さん 'okaasan'. Same goes for 父 'chichi' and お父さん 'otousan', 兄 'ani' and お兄さん 'oniisan', and 姉 'ane' and お姉さん 'oneesan'.
If you're young, or talking to close friends, then it can be permissible to use the 'o~san' words, but in formal situations you should probably use the others.