A half-sister is someone who shares the same biological mother or father, whereas a stepsister is someone’s stepparent’s daughter. To qualify as a half-sister, a person must only have a single biological parent in common.
If two people get married and one of them has kids from a prior relationship, the kids will become the other’s stepkids. The kids don’t have any biological parents in common.
The new child, however, will become a half-sibling of the elder children from each parent’s prior relationship if those two married adults conceive a child together. The new baby is the half-sibling of the elder kids because they have a common parent.