The big difference seems to be when the spice is added, with Church's/Popeye's/Indy's/Zaxby's spice added primarily before cooking/frying and the Nashville Hot added seemingly like an afterthought as something of a dry rub on top of the already fried chicken. (There are of course exceptions and variations in recipes, but that's the starting gist more or less.)
A large benefit of the Nashville Hot approach is that it is easier to spice to order/taste (most Nashville Hot restaurants are known for their numbered spice scale, they way that Thai is also typically known for its spice) rather than try to hit a consistent spice target. Which means that by default a Nashville Hot place "mild" may be less strong that Popeye's comparable "mild", but also that the scale goes to spice extremes that a Popeye's wouldn't try for fear of lawsuits. The article mentions that Prince's has spice levels that they only allow for carryout and will not allow people to eat on premises for fear of bothering other customers. I've seen Nashville Hot joints require certain spice levels to be accompanied by a glass of milk and for the eater to wear disposable gloves while eating.
It's generally lard/butter based, so calling it a dry rub is not technically correct, but watching it applied that still feels like a close enough approximation of an analogy.
Also, thought I should add the disclaimer I'm from Louisville, KY so most of my experience of Nashville Hot is definitely filtered through Hipster Fad lenses, so I am very much not an expert on the subject and you can take my knowledge with a grain of salt.
A large benefit of the Nashville Hot approach is that it is easier to spice to order/taste (most Nashville Hot restaurants are known for their numbered spice scale, they way that Thai is also typically known for its spice) rather than try to hit a consistent spice target. Which means that by default a Nashville Hot place "mild" may be less strong that Popeye's comparable "mild", but also that the scale goes to spice extremes that a Popeye's wouldn't try for fear of lawsuits. The article mentions that Prince's has spice levels that they only allow for carryout and will not allow people to eat on premises for fear of bothering other customers. I've seen Nashville Hot joints require certain spice levels to be accompanied by a glass of milk and for the eater to wear disposable gloves while eating.