A few days ago I ran into her in the library and we haven’t seen each other in like 12 months but her appearance changed and it kind of made me :reigen-sweat: We just talked and caught up, but a pressing question was in the back of my mind the whole time, which is the title of this post.
We usually just refer to each other as “cousins” when talking to other people because it was easier than explaining the family tree. No, I don’t plan on doing anything with her. We don’t have much in common and we grew up together so it’s weird even if she wasn’t related to anyone in my family. But, I am normal right?
I don't think there's a technical word since they wouldn't belong to your family tree, at least from a consanguinity perspective. As you say, your first cousin shares at least a grandparent with you. However, if (for instance) their mother is a sibling of one of your parents but their father is not (one would hope), their paternal cousins have no more genetic relation to you than any random person on the street. And of course, their maternal first cousins are the same as your first cousins.
Cutesy name I saw for it is "cousin-in-law" which does capture the difference.