It comes down to how close is the closest common ancestor. For first cousins the closest common ancestor was a grandparent, for second cousins it is a great-grandparent, etc. If there is a generational difference, you use the closer connection. Example: if Alice’s grandparents were also Bobs great-grandparents, they would be first cousins.
The ‘removed’ part is where the generation separation comes in. In the above example, Alice and Bob are different generations from their common ancestor (grandparents vs great-grandparents), so they would be first cousins once removed.
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