A subject that seems to cause much confusion in the family history community is relationships. Most people are comfortable with the terms “parent”, “sibling”, “grandparent”, “uncle”, “aunt”, “nephew”, and “niece” but can find “cousin” a little confusing. This is because it is a more general term and can cover a number of different relationships.
In the most general sense “cousin” has been used to mean any relationship, especially one that doesn’t have a more specific name. In modern times the term is more specifically used for a relationship where the two people share common ancestors that are grandparents or further back.
The most common usage is to refer to the children of aunts and uncles. Strictly these are more correctly referred to as “first cousins”. There are also “second cousins”, “third cousins” and so on. Any of these terms can also be used with the phrase “once removed”, or “twice removed” etc. This tends to be where confusion starts to arise. The term “cousins” can refer to any or all of the these relationships, but usually implies “first cousins”.
“First cousin” is the term for children of aunts and uncles. It follows that the common shared ancestors for this relationship are the grandparents. If A and B are first cousins then they share a common set of grandparents.
As an example John and Jamie are my cousins because John and Mary are grand parents to all of us.
Similarly, “second cousins” share a common set of great-grandparents. “third cousins” share common great-great-grandparents, “fourth cousins” share 3xgreat grandparents and so on. i.e. “Nth cousins” share a set of (N-1)xgreat grandparents.
But what if A and B are not of the same generation? For example, if A’s grandparents are B’s great-grandparents? This where the “removed” part comes in. The number of times removed is the number of generations difference between A and B. Thus in this example A and B are once removed.
In a case like this the greatest confusion arises from considering whether A and B are first cousins once removed or second cousins once removed. Logically, from A’s point of view the shared ancestors are grandparents and thus the relationship is first cousin, with B being one generation further down the line (i.e. once removed). From B’s point of view the shared ancestors are great-grandparents and thus the relationship is second cousin with A being one generation up from him (i.e. once removed). In the past this may have been expressed as “second cousin once removed upwards”. Both views are equally correct.
These days the usual convention is to describe the relationship using the lowest cousin number. So in the case above the relationship between A and B would be first cousin once removed.
Extending the previous example, the famous singer Dame Clara Ellen Butt is Frances' first cousin because James and Mary Ann are grandparents to them both. But from above you can seen that Frances is my great-grandmother and thus James and Mary Ann are my 3xgreat-grandparents. Dame Clara Butt is therefore my first cousin three times removed, because I am three generations below Frances.
The final complication that I shall mention is the case where only one of the grandparents is shared, not both. This happens when the shared grandparent has had children with two different partners. In this case the relationship can be described as "half-", but often this complication is ignored.
So to recap: If two people share common grandparents then they are first cousins, if they share great-grandparents they are second cousins, if they share 2xgreat-grandparents they are third cousins and if they share Nxgreat-grandparents then they are (N+1)th cousins! If the number of generations is different down each of their lines from the shared ancestors, then the lowest cousin number is used and the difference in the number of generations is the number of times removed.
I hope that all makes sense!