What I see, there are just some differences in the US vs UK. In the UK there seem to be rabbit warrens were people use ferrets and dogs. I've never seen a rabbit warren in the USA.
George Washington, Thomas Jefferson, and those guys were all into packs of hounds for hunting foxes and had terriers to get them out of their dens, but this faded greatly, and honestly as the wilderness got tamed the immigrants were Norwegian, Swede, German, etc. so foxing was just not as integrated into our culture, both hound and terrier. Many foxhounds morphed into coonhounds. Or foxing terriers morphed into rat terriers or feists.
Are you familiar with Feists? Fiest came about from blending traditional terriers and hounds. It's a 'cousin' of the rat terrier, and both types have influenced eachother. These are dogs that are fairly generalist hunters that appear quite terrierlike except often with longer legs. They are used singlely or in pairs or in packs from everything to treeing mountain lion and bear to ratting, but mostly were developed for squirrel hunting.
There are still those who hunt foxes with hounds and terriers. ALSO There are still those who send small terriers into dens and dig them out as necessary, however, most 'terrierwork' in the USA is rat terriers above ground going after rats, and secondly feist type work.