A child is referred to as the stepchild, stepdaughter or stepson of their biological parent's new spouse, and that person as the stepparent, stepfather or stepmother of the child.
A stepfather is the husband of someone's mother, and not someone's biological father.
When both members of the couple have at least one pre-existing child, the new family is "complex" or "blended" from the start; if only one member has one or more prior children but the couple has another child together, the "complex"/"blended" designation replaces the "simple" designation upon the birth of the new child.
If both members of the couple have prior children, those children are stepbrothers and stepsisters to one another.
Either one parent may have children from a previous relationship.
A step-grandmother is the wife of someone's grandfather, and not someone's biological grandmother.
A step-grandfather is the husband of someone's grandmother, and not someone's biological grandfather.
The biological parents (and, where applicable, adoptive parents) hold that privilege and responsibility.
If the biological parent does not give up their parental rights and custody of the child, the other parent's subsequent marriage cannot create a parental relationship without the biological parent's written consent before a "child" reaches adulthood.
However, in modern Western culture it is often unclear as to what, if any, social status and protection they enjoy in law.