What is a great-niece or great-nephew?
Your great-niece or great-nephew is the child of your niece or nephew, which makes them your brother's or sister's grandchild.
Preset to this relationship. Change the steps to compare with neighbouring relationships.
They are your
great-niece/nephew
Common ancestors: your parents. Expected shared DNA: 12.5%
One of you is a child of the shared couple, so this is an aunt/uncle–niece/nephew line rather than cousins.
Grand-niece and grand-nephew mean exactly the same thing. As with grand-aunt, genealogists sometimes prefer the "grand" form because it lines up with grandchild.
You are their great-aunt or great-uncle. Expected shared DNA with a full great-niece or great-nephew is about 12.5%, the same as between first cousins.
One generation further down, your niece's grandchild is your great-great-niece (or great-grand-niece).
To check a real pair of relatives, add them to the family tree maker and use How related?, or look them up on the cousin chart.
Questions
Is a great-niece my sister's granddaughter?
Yes. Your sibling's granddaughter is your great-niece.
What is my great-niece to my children?
Your children's first cousin once removed.