Interesting.
That's the first time I have ever heard anyone say there were four models. I have a bunch of Winchester books and they all say three models. This of course does not include the three different configurations that most Winchester lever guns came in; rifle, carbine, and musket.
I have two Winchester books by Madis, the small Winchester Handbook, and the much larger, much fatter book titled The Winchester Book. In the Handbook he specifically states there were three models, defined by the three different styles of dust covers. Because it is not quite as big and heavy, this is the book I usually grab when I want to look up something about Winchesters.
I must admit I have not read every page of the much more in depth The Winchester Book, it is over 600 pages. Turning to the 1873 section on page 133 he does refer to an Early First Model, a Later First Model, the Second Model, and the Third Model, with an accompanying photo and a brief description. Perhaps you have this book too. In both books he shows a photo of dust covers with 7 variations, although he does still define the 3 Models by the three styles of dust covers.
There were of course many large and small design changes to the Model 1873 in its long production life of 1873 to 1923.
Anyway, I believe most collectors categorize the 1873 Winchester as having been produced in three models, and that is how I will continue to refer to them.