"Cousin" is a vague claim. A parent is 50% similarity, a simple first cousin is typically 12.5% but may be higher if they're also related on the other side (e.g. Einstein married a woman whose parents were, respectively, a sibling of one parent and a cousin of the other, that's a lot of shared DNA). But second cousins may be only 2-3%.

So there's a huge gap between "Your mum and dad both have twins, and there was a double marriage, so, she's your first cousin twice over" and "She's your great-aunt's child's youngest" and yet you might get told both people are your "cousin" for lack of convenient terminology.