There is no word in the English language for a relationship between grandmothers of related grandchildren
John Wilkes Booth had no children, therefore no grandchildren, great grandchildren or other direct descendants.
Buchanan did not have any grandchildren-- he did not even have any children.
Your great-grandmother's sister's grandson is your second cousin once removed.
Your daughter's son is your grandson and you are his grandparent.
President John Tyler had the most children, with 15 from two marriages. He has numerous grandchildren and great-grandchildren due to the many children he has, including one still living grandson, Harrison Ruffin Tyler. Quite a feat considering served as President from 1841-1845 and died in 1862 himself.
There is no relation between you and your grandmother's cousin-in-law's grandson.
Your great great grandmother's sister's great great grandson is your third cousin, twice removed.
Not yet, but her eldest grandson is recently-married.
Your grandmother's sister's grandson is your second cousin.
Your great grandmother's brother is your great great uncle. Your parent and the grandson of your great great uncle are Second Cousins. Therefore you and the grandson of your great great uncle are Second Cousins, once removed.
Your grandmother's first cousin's grandson is your third cousin.
Your great grandmother's brother's great grandson is your third cousin.
Your grandmother's sister's daughter's grandson is your second cousin, once removed.
Your grandmother's sister is your great aunt.
The son of your grandson is your great grandson. You are his great grandmother or great grandfather.
Your great grandmother's first cousin's grandson is your third cousin once removed
Your great-grandmother's first cousin's grandson is your third cousin once removed.