There are a variety of hounds developed to accompany man on the hunt, which can be divided into three main categories. Sighthounds are incredibly fast and chase prey down, using their eyes as their main tools for locating prey; these hounds will kill the prey themselves, not waiting for their human handlers. Scent hounds are not as swift as sight hounds, but have an incredible amount of endurance; these dogs do not need to see the prey, but follow its scent. They usually signal to the hunter when prey has been found so that the hunter can kill the game. Lastly, there is the category of hounds with no distinct name, in which you find dogs that can hunt using both scent and sight.
Many scent hounds have very similar appearances: long, pendulous ears, droopy eyes that give them a soulful look, long snout and large lips. These are all characteristics that aid the scent hound in finding and tracking odors. There are a few scent hounds that look very much alike and this is probably due to a close ancestral relationship, though the details of the relationship (who is whose ancestor or descendant) are unclear. Three of these strikingly similar looking dogs are the Foxhound, Harrier, and Beagle; they look like the "small", "medium" and "large" varieties of the same dog. Are they the same dog? Is size the only thing that distinguishes them?
Not really, no. While size is definitely one of their distinguishing characteristics, it is not the only thing that differs among the dogs. For one, they were not all bred to hunt the same prey. The Beagle and Harrier were developed to track rabbits and hares and other game that did not move swiftly, but rather employed tactics such as hiding in burrows and outmaneuvering the dogs. For this reason, these two breeds are not extremely fast dogs and can be followed on foot by hunters who can't afford horses. The Beagle and the Harrier were the favorite of poorer hunters for precisely this reason. The Foxhound, on the other hand, was bred to chase foxes, a favorite prey of the nobility; foxes were not only wily but very fast and so Foxhounds were bred for speed. Wealthy individuals could also afford horses on which to follow the Foxhounds and so their speed was never a problem.
All three dogs needed a well-balanced temperament that included friendliness towards people and other dogs; hunts were very social events that included participants of both the human and canine kind and any dog that showed aggression was immediately expelled. Given this, though, there are some slight differences between the personalities of the dogs. The Beagle is probably the most outgoing and playful of the three breeds, his tail constantly wagging; Beagles also love to make a show of their love for the world and their owners and are very expressive. Foxhounds love people, but are also very independent and work-oriented; all they have on their mind is the hunt. The Harrier has a personality somewhere in between; he is more jovial and expressive than the Foxhound, but does not reach the Beagle's level of exuberance.