Both terms are correct. Some people prefer one over the other. There also seem to be a regional preferences for one or the other.
The son of a great grandson is a great greatgrandson.
There is no difference between a great nephew and a grand nephew. In some places "great nephew" is the preferred term for the grandson of one of your siblings. In other palces, grand nephew" is the preferred term for that relationship.
Your nephew's child is your great niece (if a girl) or your great nephew (if a boy).
Your nephew's son is your grand nephew or great nephew.
Your nephew's grand son is your great great nephew and you are his great great uncle (or aunt)
Your nephew's baby would be your grand-nephew or grand-niece. You would be their grand-uncle or grand-aunt.
Your great great nephew's child is your great great great niece or great great great nephew, depending on the sex of the child.
He would be your grand nephew; you would be his great-aunt.
you would be the child's great aunty or uncle Therefore, they would be your great niece or nephew.
Yes. Your grand nephew, also called great nephew, is the grandson of your brother or sister.
Your nephew's son is your grand nephew or, some would say, your great nephew. You are his great aunt or great uncle.
Your nephew's son is your grand nephew or great nephew. Some people say one, some say the other.