In the northern part of the U.S., the name is consistently written Nale. In the south, it was Nail as early as the 1700's in Virginia. I have not found a connection between the two families so far, but there may be one.
The southern Nails moved from Virginia to Georgia and then spread westward from there. Many of them could not read or write, so they left the spelling of the name up to census takers and court officials, so there are often different spellings of the name for the same person. Your branch of the family changed the spelling to Nale with George W. No reason that I know of, it just happened.
I found one instance in Tennessee where a Nail child went to school and was informed by his teacher, that he was spelling his name wrong, that it should be spelled Nale. Since they figured the teacher should know, they changed it.
The moral of the story is, look for any possible spelling for the name, because it's probably out there somewhere.