Children who share the same mother but different fathers are called half-siblings, or half-brother or half-sister depending on their gender. Half-siblings may also be two children who share the same father but have different mothers.
Traditional siblings are children who share the same mother and father. Step-siblings are children whose parents have married after the childrens' births, and there is no biological relation between the children. Foster siblings are children raised together in the same foster home, and adoptive siblings are two children who are not biologically related but were adopted by the same parents. Cross siblings are two children who share one or more half-siblings but are not related.