It seems like a struggle to me to classify cousins into first, second, third, once removed, etc.
It was always obvious to me that my first cousins were the children of my aunts and uncles. You know who you are! We share grandparents.
But who is a second cousin? They are the children of my parents' first cousins. So if my dad had a first cousin, Eldor, his children would be my second cousins.
Or, in another view, we share great-grandparents.
My third cousin would share a great-great grandparent with me, and so on, adding greats.
So, my first cousin once removed is my first cousin's child
My first cousin's grandchild would be my first cousin twice removed.
How many generations are between me and our common ancestor?
I don't know if I will ever be clear on it all, especially as it progresses further and further back in time. Maybe it's just easier to call everyone related in any way "cousin"!
Perhaps this chart from Family Search would help -