Kipling,

In addition to broadsides (sheets printed on one side only) ballads were issued in cheap print on broadsheets (printed on both sides), in small chapbooks called garlands and songsters, and on "slips" which were individual songs cut out of a larger broadside. Broadsides were also issued with other things besides songs: poems, news stories, artworks, etc.

Essentially, folklorists, looking for a classification for the ballads that came after the older, European stock (and after the Robin Hood ballads, Border ballads, and other materials collected by professor Child) began to call them "broadside ballads" because so many had been composed for publication on broadsides. The name is not strictly accurate, as there were these other forms of cheap print as well, and as not all songs so classified can be found on surviving broadsides. But it's the name that has stuck. G Malcolm Laws wrote that the ballads called broadside ballads "can either be traced to British broadsides or are clearly in the broadside style. Hence the term broadside balladry distinguishes this class of songs from the native American ballads and from those of Child."

If someone refers to the song itself as a "broadside" then that is shorthand; folklorists would say it is "broadside ballad" or "broadside song."