As I recall ( I can't go look as we have 2 foot of snow right now) the long inspection tag has sections for different parts of the car. Paint, body, interior, etc.
As it went through the line I think there would have been a line inspector that put his stamp on the inspection tag. When the car got to the end of the line they would break the
tag off at the lines that cross it. leaving nothing but a little piece under the screw and fender tag.
I wasn't there, I wasn't born. I am only going on what I have picked up over some years. This is kind of my two cents anyway from seeing so many tags.