I recently contacted someone who had posted on a surname list that he was researching Mulcahys from Pallasgreen, Limerick, Ireland. My Mulcahys, too, are from Pallasgreen, Limerick, Ireland, and I sent him a brief description of what I knew of the family to see if there was any chance we were researching the same family.
His response said he didn't think so, but he'd send me what information we had and see if maybe there was a link a generation further back than the one I'd been able to describe.
I then sent an e-mail to my uncle, John, explaining the situation and asking if he had any information about the family of Michael Mulcahy's father James. "It doesn't appear that we're closely related - he's not descended from any of Michael's siblings - but we'd like to look into Michael's aunts and uncles."
Then I stopped. Said Michael is my great-great-grandfather, which, if I'm determining the relationships correctly, would make us - if there had been a connection through Michael's siblings - probably 3rd cousins once removed. And I'd nonchalantly referred to such a cousinship as being "closely related."
Only a genealogist!