I would say second cousin though dont know if that or that first cousin once removed crap would be the appropriate term for that. Your parents first cousin could probably be considered a second cousin too. Maybe cousin would b good.
“Primo hermano (cousin sibling)” is another word if you want to distinguish between “first cousins and any other cousins”.
This wasn’t all that unusual in North America when large families were more common. In one nuclear family, the oldest and youngest siblings could be 25 years apart or more, so baby aunts and uncles did happen.
I heard a friend talking about being proud of his “couphew” Perfect! I vowed to remember it and then hope my cousin had a son. And have a son he did, and I am similarly proud of my couphew. Alas, I have no good word for his twin sister…
This thread seems like as good a place as any to wonder if there’s a non gender specific word for nieces and nephews (similar to siblings).
Son/Daughter
I’m off to NASCAR 
That would make her your couiece which I’d pronounce co-eese or kweese if you prefer.
I just call them the little cousins, or my cousins’ kids. (However, understanding and being able to explain the cousins-once-removed system is one of my few superpowers.)
No, those are in my generation, but our closest relatives are great-grandparents. I usually call them los hijos de mis primos (my cousins’ children), but strictly speaking they’re mis sobrinos segundos (my second nephews).
I used to have one of my tíos lejanos (distant uncles) as a classmate, we used to joke that we weren’t sure whether he was my tío cuarto or my tío quinto (fourth or fifth uncle). His dad and my grandma were first cousins. Since he was one generation above mine, he was my uncle and I his niece, although I’m half a year older (his sibs are all older).
I probably wouldn’t actually use the correct phrase, “first cousin once removed,” in ordinary conversation. I’d probably say, “my cousin’s kid.” But since none of my six cousins have reproduced, nor myself or two brothers, I don’t really have to worry about it.
I call him Zack.
According to Encyclopedia Americana’s article on “Genealogy”, the relationship is bi-directional only if both you and your cousin are the same number of generations from the common ancestor. If you and your cousin are different generations, the “N times removed” will be symmetrical, but the “Nth Cousin” will be different.
“Nth cousin” indicates how far back is the nearest common ancestor. And it will be different, depending on whether it is reckoned from you, or from your cousin. “N times removed” indicates how many generations apart you are.
If Joe is your first cousin’s son, he is a descendant of your grandparent, therefore your first cousin once removed. But the nearest common ancestor is his great grandparent; therefore, to him, you are a second cousin once removed.
Descendants of yourself:
son
grandson
great grandson
etc
Descendants of your parent:
sibling
nephew
grandnephew
great grandnephew
etc.
Descendants of your grandparent:
uncle
first cousin
first cousin once removed
first cousin twice removed
etc.
Descendants of your great grandparent:
granduncle
second cousin once removed
second cousin
second cousin once removed
second cousin twice removed
etc.
Descendants of your great great grandparent:
great granduncle
third cousin twice removed
third cousin once removed
third cousin
third cousin once removed
third cousin twice removed
etc.
Encyclopedia Americana has a graphic that makes it much easier to remember.
The “nth cousin” refers to how many generations back you must go to find the common ancestor, using the smaller of the two numbers. The relationship is bi-directional. For example, my first cousins and I share grandparents. The common ancestor for me and my 1st cousins’ kids is my grandparent ( and their great grandparent). We are “first cousins” because the common ancestor is a grandparent to one of us and “once removed” because we are of different generations. This Wiki entry has an easy to understand table and chart
Encyclopedia Americana is flatly, unambiguously wrong if you’ve characterised the entry accurately. It is a bi-directional relationship because you count back the shortest path to the common ancestor.
And with further reading, the asymmetric method of determining degree of cousinship exists, is considered non-standard, and (according to Wikipedia) is excluded from most major dictionaries. It is also not the method used by most genealogy packages in my experience. If the Encyclopedia Americana omitted to mention this method of determining kinship is an alternative method that’s far less frequently used, then I’m still comfortable calling that wrong.
First time I’ve ever seen this “symmetric” definition for cousins.