There is no difference.
The words are used interchangeably - some people say one in preference to the other.
The terms grand niece and great niece mean the same thing, the granddaughter of your brother or sister. Some regions, and some people, prefer one term and some prefer the other, but both are correct and understandable terms.
You are their Great Grand Nephew or Niece, which I think makes them your Great Grand Uncle. Ref: http://freepages.genealogy.rootsweb.ancestry.com/~gentutor/chart.html
my nephew had a baby...his mother is my sister...she is now a grandma which "should" make me a granduncle...and our mother is now a great grandma which "should" make her brother a great grand uncle.
great great great
The relationship is that of a great great great grand uncle and great great great grand niece
Your brother is your grandson's great uncle, and your grandson is your borther's great nephew. Some people would also say grand nephew and grand uncle.
Your great uncle is the brother of one of your grandparents, so his grandfather is also the grandfather of one of your grandparents. The grandfather of your grandparent is your great great great grandfather.
Your grandfather's brother is your great uncle and your parent's uncle.
Your grand niece's son is your great grand nephew, or, some would say, your great great nephew. You are his great grand aunt or great grand uncle, or, some would say, great great aunt or great great uncle.
Your Grand Uncle(great uncle) would be your grandmother or grandfathers brother.
Many genealogy programs include a feature that calculates relationships between family members. The relationship between a grandmother's brother and a her grandchild is "grand uncle" or "great uncle." Learn more at 23andme.com.
A grand uncle or great uncle is the brother of one of your grandparents.