They would be second cousins, once removed. The descent is from a common ancestor. Thus 1st cousins share a grandparent as a common ancestor. 2nd cousins share a great-grandparent as an ancestor. If the descent from the common ancestor is not an equal number of generations, the inequality is expressed as 'removed' from the oldest generation being compared.
You and your first cousin share a common grandparent. Your child and your cousin's child would be second cousins. The grandchildren would be third cousins.
Your sister's great grandson is your great great nephew. You are his great great uncle, or great great aunt.
Your brother's grandchild is your Great Nephew or Great Niece and you are their Great Aunt or Great Uncle.
Your son and your sisters child are first cousins. The granddaughter is out of synch by a generation. That will make them first cousins once removed.
Your sons children and your daughters children are First cousins. The idea is that First cousins share a grandparent, second cousins share a great-grandparent, third cousins share a great-great-grandparent, and so on. The degree of cousin relationship i.e. "first," "second," etc. is used to denote the number of generations between two cousins and their nearest common ancestor. Now, a term "removed" is used to refer to the number of generations separating the cousins themselves. So your first cousin once removed is the child (or parent) of your first cousin. Your second cousin once removed is the child (or parent) of your second cousin. And your first cousin twice removed is the grandchild (or grandparent) of your first cousin. etc. Thus in this case they are first cousins once removed.
Your child and your niece are first cousins to each other. Your child and your niece's child are first cousins, once removed.
Your son and your brother's grandchild are first cousins once removed.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
Your child and your nephew are first cousins, so your grandchild and your nephew are first cousins once removed.
You and your uncle's child are first cousins to each other. You and your uncle's grandchild are first cousins, once removed, to each other.
Great grandniece or great grandnephew
For clarity. let's call your grandmother's aunt "the aunt". Sequence of relationship: (1) The aunt's child and your grandmother are 1st cousins (2) The aunt's grandchild and one of your parents are 2nd cousins (3) The aunt's great grandchild and you are 3rd cousins
Your mother's sister is your aunt. Your aunt's child is your first cousins. Your aunt's grandchild is your first cousin, once removed. Your aunt's great grandchild is your first cousin, twice removed.
First cousins once removed.
Your child and your sister's child share a common grandparent and are first cousins. Your grandchild and your sister's grandchild share a common great grandparent and are second cousins. There is a generation out of synch, so they would be second cousins once removed.
Your first cousin's child's child (your first cousin's grandchild) is yopur first cousin twice removed.
The grandchild of your father's first cousin and your child (your father's grandchild) are third cousins to each other. In the US, no jurisdiction prohibits such marriages.
Your child and your sister's children are first cousins. Your grandchild and your sister's children are first cousins once removed.