What does it mean if someone says “We’re _____ cousins, twice removed”?
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This is actually really easy once you know how it works.
Start by identifying your closest blood relative in common. If that’s your parent, you’re siblings. If it’s a grandparent, you’re cousins. Great grandparent, second cousins, etc.
That’s the end of it if you both are the same number of generations from your common ancestor.
If you’re not, then the degree of your cousinhood is determined by the person closer to that ancestor. So if the common ancestor is your great grandparent, but the other person’s great-great grandparent, it goes by you, so you are still second cousins but with a degree of removal.
That degree of removal is the difference in generations from the common ancestor. In this example, since the other person is one generation more distant from the common ancestor, you two are second cousins, once removed. That person’s kids are your second cousins, twice removed.
Keep in mind that this way of describing relationships only tells you the amount of genetic material you have in common with someone (on average), it is not unique to a particular configuration in the family tree. To understand a specific relationship in detail, it’s better to track relationships simply by identifying the common ancestor instead of saying “nth cousin x removed.” IOW there are multiple ways you can be related to someone as an “nth cousin x removed.”
Now think about if your mom gets remarried to someone with kids. Those are your half-siblings, right? Same thing across the whole family tree. If you have cousins that are related to your blood grandfather’s by marriage, those are your half-cousins. If they are related by adoption instead of by marriage or blood, they are your step cousins.
Someone can have multiple relations to you. For instance, a girl might have a kid that they’re too young to raise, so an older sibling raises the kid. That older sibling is the child’s aunt, but could adopt them as a stepchild, making that person the child’s aunt by blood and stepmom at the same time. The convention is always to use the “strongest” relationship as the default one, which goes in order: blood, adoption, marriage.
Obviously in some cases the people involved may all agree that this ordering doesn’t reflect their situation, they might consider theirs a special case, which is fine but it doesn’t change the genetic relationships involved. In such a case, from a genealogical perspective, you’d want to know all of the relationships involved because genealogy is as much about the social relationships as the genetic ones.
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