Basically, the difference is whether you or your child is being spoken of.
As you know, your first cousin is the child of your parent’s sibling (your aunt or uncle). If your first cousin has a child, that child is your first cousin, one generation removed. The removed cousin takes the lowest applicable cousin number and the number of generations they are from you.
Let’s take the same situation as above; except now both you and your first cousin have children. Basically, those children are second cousins to each other because their parents are first cousins. If these two second cousins each have children of their own, those children will be third cousins.
Here are a few rules of thumb to help you keep things straight:
1. Cousin numbers indicate the number of “Gs” in the title of their earliest shared common ancestor. For example, two FIRST cousins will share a Grandparent; two SECOND cousins will share a Great-Grandparent; two THIRD cousins will share a Great-Great-Grandparent; etc.
2. If you have a removed cousin, the cousin number PLUS the removed number will equal the lowest cousin number for your descendants to the removed cousin. For example, if you have a first cousin (1) once removed (1), your child will be a second cousin to the removed cousin (1+1=2). If your first cousin once removed has a child, they are your first cousin (1) twice removed (2), and your grandchildren would be child’s third cousin (1+2=3).
[Here’s](https://youtu.be/PM79Epw_cp8?si=SwLBUL1QIMBev8oH) a video that explains it pretty well.
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