How are we related?

I tried to explain my American relatives how we are related but found it difficult to find understandable terms.

Cousin Tree

Is a <Großvater> a grandfather? Yes he is. Consequently his brother will be a granduncle?  No, he is not. He is a great-uncle. Is his grandson my <Cousin 2. Grades>? Almost. He is a second cousin to me. And his daughter? Is she a <Nichte 3. Grades> a  third niece? No, she is not. But she is a second cousin once removed. Incredibly complicated but true. Wikipedia helps with tables.
European kinship system
European kinship system