stepsister = not related by blood
half-sister = related by blood, either by the father's blood or the mother's blood.
Sue has a daughter (Mary) and Stan has a daughter (Barb). Sue and Stan met and got married, and now their daughters are step-sisters; they are not related by blood to each other. Two years later, Sue and Stan had a baby girl (Fiona). Fiona is a half-sister to both Mary and Barb. Fiona and Mary shares blood with their mother, and Fiona and Barb share blood with their father.