One of my pet peeves is a term that I see online over and over: someone claiming to be a “half first cousin” or a “half second cousin once removed” or something similar. Sorry folks, but there is no such thing as a “half first cousin” according to legal dictionaries. However, the term is used by others. I know that lots of families use that term to refer to various relatives.
NOTE: I will describe references used in the U.S. It is possible that relations are described differently in other countries and especially in languages other than English.
Many people think that a “half first cousin” is someone who shares one grandparent with you but not both of them. For instance, my great-grandfather was married twice. He had several children by his first wife. The wife then died in childbirth, and great-grandfather later remarried and had more children by his second wife. I am descended from great-grandfather and his first wife. I recently met a man who is descended from my great-grandfather and his second wife. Some people would think that this other man and I are half-second cousins. “Half” apparently refers to the fact that we share only half the relationship because of our different great-grandmothers.
In fact, we are second cousins. Period.