Someone has a half-sister if the two of them share only one parent. So, if a brother and sister are born to the same mother, but they have different fathers, then they are half-siblings. This is also true if they share the same father and not the same mother.
Some half-siblings are raised together, and some are not. Likewise, some half-siblings may prefer to refer to each other as such, while others may not. It is up to the half-siblings to determine how to define their relationship. Half-siblings that were raised together tend to be less likely to use the term.