The person who has one or more grandchildren is called a grandparent (grandfather or grandmother). The sex of the child's parent (i.e. father or mother) who is the child of the grandparent minor influences the names of the endpoints of this two-step relationship, that unless you want to be specific you can ignore.
maternal grandmother \ mother \ maternal grandfather / \ child paternal grandmother \ / father / paternal grandfather /
A child has four biological grandparents: a grandmother and grandfather of the mother's side, and a grandmother and grandfather of the father's side. In practice, it is often the case that some of these have passed away by the time the grandchild is born or grows up. A grandparent can also be unknown. Besides, a child's parent or grandparent may remarry after being divorced or widowed, which can result in non-biological (step-) grandparents.
Grandchildren and spanking
Grandchildren are often given in the temporary custody of their grandparent(s) for babysitting and other in loco parentis tasks. In families in which children get spanked for misbehavior, it is not uncommon that the grandparent(s) use the same parenting methods while the grandchild is in their care. Often the grandparent(s) will be more lenient, while in other cases they may be stricter than the parents.
In the latter case, they may use old-fashioned disciplinary methods that were common in their own childhood days. This subject matter is often found in spanking art and spanking stories on the grandparent-grandchild topic.