What constitutes a second cousin and other family relations?

Yes. Agreed, but to answer more fully, second cousins are from the bloodline of a common great-grandparent. Put another way, Person A and Person B, the second cousins, each have a grandparent who had at least one parent in common. (This might occur if one parent remarried and that couple gave birth to another child). If they had both parents in common, such second cousins are sometimes referred to as "double" second cousins, but most people don't get that technical. Therefore, to be clear, even grandparents who are only half-siblings would still have grandchildren who are second cousins. There is no such thing as a "half-cousin" relationship. Cousin means you are related by blood through a common relative, one - period.