A stepsister is the daughter of one's stepparent, while a half-sister shares the same biological mother or father. A half-sister can only share one biological parent to be considered a half-sibling.
If two adults marry, and each has children from a previous relationship, those children will become step-siblings to each other. Neither of the children shares a biological parent.
However, if those two married adults have a baby together, that new baby will become the half-sibling of the older children from each parent's previous relationship. The older children share one common parent with the new baby, making the baby their half-sibling.