This sounds like it is one in the same. I am a descendant of Thomas Jefferson Adair, through his daughter, Mary Ann Adair. She married John Mangum III. I do have some information about this family, and I would love to share what I know and learn what you know. I don't know when Joseph Adair was born, nor where he was born or where he died. I do know his father and a little about that.
Thank you again for your reply. I hope to hear from you soon.