Both names describe someone from your grandparents' generation, and they get mixed up all the time. They are different people.
Great-aunt or great-uncle
A great-aunt is the sister of one of your grandparents. Work through the counts: the shared ancestor is your grandparent's parent, three generations above you, so a is 3. The great-aunt is that ancestor's child, one generation down, so b is 1. See the terms list for the great-uncle line.
First cousin twice removed
A first cousin twice removed, on your grandparents' level, is a first cousin of one of your grandparents. Your grandparent and that cousin share a pair of grandparents, who are your great-great-grandparents. So a is 4 and b is 2: the degree is 1 and the removal is 2.
How to tell them apart
- If they are a sibling of a grandparent, they are a great-aunt or great-uncle.
- If they are a cousin of a grandparent, they are a first cousin twice removed.
- If they are the child of a great-aunt, they are a first cousin twice removed in the other direction: a is 3 and b is 2.
Many people say "great-aunt" for any older relative of that generation out of respect, which is fine in family life, and still not what the genealogical name means. Try both in the calculator, then read the pages for first cousin twice removed.