Question: A woman had a child by her first marriage, and a man had a child by his first marriage. They married each other and are now having a child together. Now I know that these children mentioned above are step-siblings to each other. Is this newborn child of the couple a step-sibling to both their firstborns?
The newborn child will be the HALF-SIBLING for both sides. Half siblings are NOT step-siblings. Step-siblings have no genes (DNA) in common because none of their parents are common, but half-siblings do share half of their genes with each other since they are biologically connected through one parent.
A half-sibling may be different from a full-sibling in the aspect of inheritance (depending on who the legator is), but it is the same as a full-sibling in the aspect of mahram relations, such as marriage, observing the hijab, etc.