What would I call my dad's uncle's son?
Your father's uncle's son is your first cousin, once removed. He is your cousin because of the relationship between you, your father and your father's uncle. You are directly related through blood and all originated from a common grandparent. First cousins, as the sources linked to below indicate, share a common grandparent. Because your father and his uncle are directly linked through your grandparent, the father's uncle being a sibling of the grandparent, the father's uncle's son is your first cousin. The first cousin is "once removed" because of the generational difference between you and him. Your father and his uncle are of different generations, and your father's uncle's offspring would, consequently, be of a different generation than you. Those offspring, in fact, would be on the same genealogical plane as your father. You and your father are of different generations; therefore, the son of your father’s uncle would also be in a different generation than you, which makes you the son’s cousin once removed.
The son of my father’s uncle is called my first cousin once removed. This is because he is my father’s first cousin and I am one generation removed from the generation that they are in.
My father’s uncle is the brother of my father’s father. His son is my father’s first cousin. They share a common grandfather, thus making them first cousins. By the rules of how we name relationships, this makes me and my father’s cousin first cousins as well. However, we are not of the same generation. Instead, I am one generation removed from them. Therefore, we are first cousins once removed.
Now, if my father’s uncle’s son has a child, that child and I are not first cousins. Instead, we are defined as second cousins because our common ancestor is our mutual great-grandfather.