2nd cousins
When one person's great grandmother is the another person's great aunt, the relationship between the two people is that of second cousins, once removed.
When two people have the same great grandmother, depending on whether they also have other, closer, relatives in common they could be:siblingsfirst cousinssecond cousins
Where Joe's great-great grandmother is also Jane's great grandmother, Joe and Jane are Second Cousins, Once Removed. (Joe's parent and Jane are Second Cousins.)
Your grandmother's brother is your children's great-granduncle (or great great uncle). They are his great-grandnieces and great-grandnephews.
Your great-aunt
Your grandmother's brother is your great uncle and you are his great niece or great nephew. Your child is his great great niece or great great nephew.
The grandson of your great grandmother's brother is second cousin to one of your parents, and your second cousin once removed.
Your grandmother's sister is your daughter's great great aunt. Your daughter is the great great niece of your grandmother's sister.
If the great grandmother of one person was the great great aunt of another, the two are third cousins to each other.
Your great grandmother's brother's great grandson is your third cousin.
Your grandmother's sister is your great aunt.
Your grandmother's brother is your great uncle. You and your great uncle's grandchild are second cousins to each other. Your and your great uncle's great grandson are second cousins, once removed.