Isn't it Grand?

I've always referred to my neice Desiree, and nephew Anthony's kids as my great-nephew or great-neice. While talking to someone at work yesterday, they told me that actually, they were my grand-neices and nephews, and that their children would then be my great-grandnephew or great-grandneice.

I thought about it, and I guess it makes sense.

David is Mary's grandson, and she is my sister, so I'm not his grandmother, but I guess I would be his grandaunt.

My mom is Katie's great-grandmother, so I guess when Mary's grandkids have children, they will be her great-grandchildren, and my great-grandnephews or neices.

So do I now start introducing David as my grandnephew and Hannah as my grandneice? I looked it up in google and found that in America, it's still referred to as great-nephew, but in Brittian, they do Grand. I think, after considering it, Grand makes more sense, since Grand indicates 2 generations away (mom, grandmother) while great indicates 3 generations distance (mom, grandmother, great-grandmother), why should David and Hannah, who are only 2 generations away from me (neice, David--nephew, Hannah) be great? If Katie calls me grandma, shouldn't David and Hannah consider me as grand Aunt?