It’s pretty hard to tell the difference between Treeing Walker coonhounds and foxhounds. Most of the differences are behavioral rather than visibly structural, and the behavioral differences are most evident in a hunting setting.
Both American foxhounds and coonhounds had the same ancestors--hounds brought from Europe to the Americas in colonial days. In Europe, desirable game did not climb trees to get away from hounds. Hounds were mostly used to chase deer and foxes. In the Americas, gray foxes, raccoons, opossums, black bears, bobcats, and mountain lions all climb trees when they want to get away from hounds, so American hunters selectively bred those hounds that looked for scent on trees and barked at treed game, holding it there for the hunter.
The offspring of this selective breeding became the coonhound breeds. The tri-colored coonhounds, the ones that look oversized beagles, were separated out as an individual breed, Treeing Walker Coonhounds, in the 1940’s. Approximately half of all purebred coonhounds in the United States are Treeing Walkers, with the other half divided between the remaining five or six breeds.
The formal mounted foxhunts generally use a sturdier looking hound that is heavier than a typical coonhound with slightly shorter ears. Two such strains are the American and the English Foxhounds. Foxhounds trained to hunt in large packs, like those that hunt with the mounted hunts, are more deferential and are less likely to be terribly independent.

Within the individual breeds, there are a number of "strains" or "bloodlines" that you wouldn't be able to tell apart without seeing their pedigrees.
When it comes to coat color, very few treeing Walker coonhounds are almost entirely white, although there are some, particularly those in the Clover bloodline. In general, a dog that is almost entirely white, with just a little sprinkling of other colors, is most likely a foxhound. There was an old time French breed of hound called a porcelaine that was almost entirely white. However, dogs of many breeds with predominantly white coats may have a genetic tendency to deafness, so they are not necessarily the best breeding stock.
Coonhounds that have been bred to look up trees often throw their heads way back when they bay, and are very given to putting their front paws up on anything handy—a tree with game in it, a kitchen counter, some stranger they are greeting effusively. This is bred-in behavior, but can be modified. A pet coonhound can and should be trained to stay off the kitchen counter and not jump on strangers.
I have a lot of experience with hounds of all kinds, and even I have trouble recognizing the difference between coonhounds and foxhounds without seeing their papers or watching them work.
At Coonhound Companions, we're working hard to find pet homes for the failed hunters. In the right home, where their loud voices are appreciated and their affectionate loyal natures are reciprocated, they are extremely good pets.