It appears that Wagner, Griswold, and Lodge all had the same model numbers for their skillets, ranging from 2 to 14, with 2 being the smallest and 14 being the largest.
However, the model number is not to be confused with the actual size of the skillet. They are different.
Each brand's model numbers are approximately the same size, within a quarter to a half inch.
The #3 skillet is approximately 6 1/2 inches.
The #5 skillet, approximately 8 inches.
The #8 skillet, approximately 10 1/2 inches.
The #10 skillet, approximately 12 inches.
The #12 skillet, approximately 13 1/4 inches.
The #14, approximately 15 inches.
Any model in between those numbers, are somewhere in between the respective sizes.
There's a great illustration of skillets and their model numbers at the following link:
I also just discovered a skillet and dutch oven size and capacity chart at the following link:
Apparently, the numbers referred to what size stove eye the skillet heat ring would fit in.
Since most of us no longer use wood or coal stoves, that's no longer relevant.
Griddles had a different size / diameter standard, but I haven't found a chart for that yet.
I do know that a #6 is about 8 1/2 inches, a #7, about 9 inches, and a #9, about 10 1/2 inches.