Let's assume you are talking about first cousins.
If they are children of the same cousin they are siblings (brothers and sisters).
If they are children of different cousins and the cousins are both children of the siblings of one of your parents, then the cousin's children are second cousins to each other.
If one of the cousins is a child of a sibling of one of your parents and the other cousins is a child of a sibling of your other parent, then the cousin's children are not related to each other.
If you are talking and the children of second cousins, they children are siblings, third cousins or not related.
If you are talking about cousins who are once, twice or more removed from you, the possible relationships become too complex to discuss here.
Your child and your niece are first cousins to each other. Your child and your niece's child are first cousins, once removed.
Your child and your nephew are first cousins. Your child and your great nephew are first cousins, once removed.
Your uncle's granddaughter and your child are second cousins.
First cousin once removed.
You and the child of your second cousin are second cousins, once removed.
Your first cousin's child and your child are second cosins. Your first cousin's grandshild and your child are second cousins, once removed. Your second cousin's child and your child are third cousins. Your second cousin's grandchild and your child are third cousins, once removed.
Your second cousin's siblings are also your second cousins. The children of your second cousins are your second cousins, once removed.
Your child and your great nephew's parents would be first cousins. Their children would then be second cousins. And if they have children, they will be third cousins.
Your daughter and your sister's child are first cousins. Your daughter and your sister's grandchild are first cousins, once removed.
They are of no blood relation. But they are cousins by marriage or 'step-cousins' as such.
Your first cousin's child is your first cousin once removed. Your second cousin's child is your second cousin, once removed.
Your daughter and your niece are first cousins. Your daughter than your niece's son are first cousin's once removed. Your daughter's child and your niece's child are second cousins to each other.