Jabblog has done a post about family and birthdays, and has provided an excellent explanation of cousins, second or otherwise. So I did a very abbreviated family tree so I could identify the status of my various and numerous cousins.
I've always assumed my cousins were all second cousins but it seems lots are first cousins once removed. And here's the explanation from Jabblog:
Your second cousin is someone who shares a great-grandparent with you.
Your first cousin once removed is either the child of your first cousin, or your parent’s first cousin.
So now you know.