There is a bit of a difference. One is more of a "hey, that guy has the same name as me" thing and the other is a "speak not the name of the unclean one lest the FBI put you in their book of doom as well" thing.
She's one of those talking heads who just plays devil's advocate with everybody she talks to. I'd be surprised if she's ever actually stated her real opinion on air. She's just trying to trick her guests into arguing with her. Piers Morgan is the same way.
I was hoping this video would feature a Nancy Grace splitting out of Nancy Grace's mouth, which then had another Nancy Grace emerge out of its mouth, over and over again like a Cyriak gif in a never-ending cycle of pain.