Your cousins child is your first cousin once removed.
They are cousins.
Your child and your first cousin's child are second cousins. Your child and your second cousin's child are third cousins to each other.
Your son's child and your nephew are second cousins.
You are second cousins
they would be cousins.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
The relationship between your sister's (or brother's) child and your cousin is the same as the relationship between your child and your cousin. Your child and your first cousin are first cousins, once removed. Your child and your second cousin are second cousins, once removed, and so forth.
Your child and your sister's daughter are first cousins. Your grand child and your sister's daughter are first cousins, once removed.
Second cousins.
Your son and your 1st cousin's child are 2nd cousins.
Your sister's child and your grandson are first cousins once removed.
Your first-cousin and your child are first cousins, once removed.