If I’m being technical, I call them my first cousins once removed.
However, in my mother’s family, large families are pretty common. Mom is #5 of 14 and had five of her children at or after 30. Her youngest siblings are closer to my age than hers. They have nieces and nephews who are actually older than they are. Granny’s family was similar; Mom has first cousins my age. This leads to kids calling anyone who seems old enough to be parents (or older yet) Aunt or Uncle and anyone around their age cousins, regardless of the degree.
In Chinese culture AFAIK the kid would be thought of as one’s nephew or niece and you would be the aunt/uncle. It’s thus not uncommon for people to be required to address someone as “uncle” or “auntie” when that person is actually the same age, or younger.
OTOH, I think referring to the OP’s relationship as “second cousin” just reflects ignorance.
If if matters to the story, I describe the relationship. Otherwise, though, the general ‘cousin cousins’ category—not your by-definition cousin, but those related by cousins.
ETA: that’s actually when I’m talking about that child’s relationship to my child. Relationship to me is just “my cousin’s son.”
In my case the generations are tight. My cousins are close to my age, their kids are close to my kids age. However, the family isn’t at that level. I don’t see my cousins kids often enough for them to have an “aunt” relationship, nor do I think of them as my cousins, who are those kids I played with thirty odd years ago.
I think people get confused because the default connotation of cousin is of someone who is related to you and who is somewhere around your own age, give or take. What’s more the term first cousin, even with “once removed” or “twice removed” tacked on suggests a particularly close degree of consanguinity, even though that impression may be false. My family genealogy lists a number of people who would be my first cousin ten or fifteen times removed, but the degree of actual relatedness between them and me is minimal.
I have a cousin who insists on calling my father ‘Uncle Nekodad’.
Which cracks my father and this cousin’s father up.
The reason?
This cousin is a first cousin once removed - he’s dad’s first cousin.
But he’s the same age as me, and his father is only a little older than mine, so my dad reads as his uncle. (Especially since Dad and Uncle Ed were really close when they were younger.)
My mother is painstakingly precise in these things, and we’re from a [del]large[/del] huge extended family (descendants from a large polygamous family) so I grew up thinking everyone knew what first cousins, once removed meant and that would be part of normal conversations. Now I just use “my cousin’s kid.”
Asked my Taiwanese wife what they do, and she said she’s got an uncle who is younger than her. Technically, she should call him “uncle” but they just use first names.
The relationship is bi-directional. If Charlie is Bob’s first cousin once removed, then Bob is Charlie’s first cousin once removed. You count the shortest path back to siblings to get the cousinship, and the generations between them to get the degrees removed.
Five generations in a thoughtfully alphabetical family might look like this:
Gen 1: Alan married Amy
Gen 2: siblings Bob and Bertha
Gen 3: Bob’s son Charlie, Bertha’s son Cameron
Gen 4: Charlie’s daughter Debbie, Cameron’s daughter Diana
Gen 5: Debbie’s daughter Emma, Diana’s son Ethan
How are Charlie and Ethan related? There’s only one step back from Charlie to find siblings Bob and Bertha (you always follow the shortest path), so they are first cousins, then Ethan is two generations further down so they are first cousins twice removed.Ethan and Emma have to go back three generations to find siblings, so they’re third cousins; no removes because they’re in the same generation. Emma and Diana are second cousins once removed.
I refer to cousins of any degree as “my cousin” in general conversation (on Facebook, my cousin Mike from Georgia, USA is actually my 9th cousin once removed - our mutual ancestors were a couple married on the 4th of Feb 1666 in Cornwall, England), but I get the twitches to hear people saying second cousin for everything from first cousin once removed to cousin of their cousin and no actual blood relation whatsoever.
And Spectre of Pithecanthropus, your first cousins ten or fifteen times removed are highly unlikely to be living people. If you’re not speaking of the long-dead (or the not-yet-born), is it possible that they are tenth or fifteenth cousins? Generations break down over time, when oldest children have kids young and youngest children have kids late making it possible for two people related as something like fourth cousins five times removed to be living simultaneously, but a first cousin fifteen times removed being alive at the same time as you is only fractionally more likely than his mother, your great, great, great, great, great, great, great, great, great, great, great, great, great, great, great, great aunt, still being alive.
From my Dads side I call one of his first cousins “Uncle” and he thinks and refers to me as a nephew and he is close enough to us that the description is accurate. Another cousin of my fathers is someone I have met twice in my life an I just refer to him by name and have never needed to call him anything to his face. One of my mother’s sorta cousins who we are also close to is 5 years younger than me and I call her by her name.
I must admit that it might be a cultural thing, but I do feel strange calling someone my parents age a “cousin”. If you are close than Uncle, Aunt is good enough, if not than “Mr and or Ms SoandSo”. After all, the term depends on the relationship not consanguinity.
This, for the ones that I interact with semi-regularly. For the cousins that I only see every five Christmases or something, their kids are “my cousin’s kids.”
That’s ironic, because “primo” means “(first) cousin” nowadays (as well as “first”), but used to just mean “first”… and was then part of a two-word phrase, but the word in the phrase which just meant “cousin” fell into disuse.
(I can’t recall offhand what that word was…it may have fallen into disuse as long ago as Late Vulgate Latin times.)
When they’re still young enough to be an extension of my cousin (ie., can’t drive themselves to a gathering or decide whether or not they want to go) they’re my cousin’s kid, but otherwise, they’re my cousin. I think the distinction for me is because of the huge age gap in my family, some of my cousin’s kids are closer in age to me than the cousins themselves. I’m the youngest first cousin on each side of my family.