This is what my grandpa found out. Some ancestor around 200 years ago was given our family surname but their Y-DNA didn't match. My grandpa and his cousins (who've now had their Y-DNA analyzed) have the same Y-DNA of another family (our genetic surname, if you will) so they're all related, just not the descendants of their family surname. We laugh about it because we know what the genetic surname is, so we've been tracing where our family surname and the genetic surname had interactions. Sometime between the American Revolution and about 1820 a bastard was born (among other theories)...