Hog Run probably refers to when out west they would herd the hogs from an area to a marketing yard next to the railroads.
Hogs are a difficult animal to "run". They have short legs: mean that when walked any great distance, they lose a relatively high percent of their (marketable) body weight. They are not docile: some are so ornery that their eyes would be sewed shut for the run, lest they bolt and lead other hogs after them.
Because hog runs were difficult, hog were often slaughtered near where they were raised. They would be carried log-distance to martket as preserved pork (usually salt pork), not as a live pig. End-consumers thus became used to buying pork that had been slaughtered long previously, and so, when railroad technology became available for long distance transport, such "dressed" pork did not face market resistance.
Beef marketing, however, was quite different. Since cattle can more practically be walked long distances, it was typically delivered to the ultimate market "on the hoof". Even in a city far from the cattle's range, the retail buyer got beef which had been slaughtered only days before.
When railroads came, it became more economic to ship beef after slaughter rather than as part of a live cow. (Why pay to ship the non-meat parts of the cow, which total about half of a cow's weight?) But it took great marketing effort to overcome customer distaste for "non-fresh beef". There were also major battles over freight rates as the eastern beef industry, to protect its business, lobbied hard to have a high shipping charge-per-pound set for dressed beef coming in from the west.
