The hellhound is a dog-like entity that commonly occurs in folklore, fiction, and mythology. They appear in a variety of different myths and folklore from different cultures. It commonly manifests as a large to massive dog with glowing red eyes. It often can appear and disappear at will. Some legends say that if you see or gaze into the dog's eyes 3 times or more, you will die. With this, the dog could be known as an omen of death. This entity could also be connected or related to the Black Dog Ghost that appears at night, and is often depicted with black fur, and glowing eyes. It commonly appears at crossroads, and during electrical storms.
My personal view on Hellhounds is that it is just a term to describe an apparition of a dark, ominous, dog-like entity. The legend may not necessarily be true, but it is quite an interesting topic to read about, since there isn't a lot to go on. This entity may be an omen, an entity, or just a spooky tale or Urban Legend. This may vary through belief in the hound.
There are a few examples from mythology that could possibly be related to this dog. Cerberus (Hound with three heads) from Greek mythology, and Garmr from Norse mythology. There are various black hounds that all seem to be slightly demonic or hellish in mythology. Cu Sith is a Scottish otherworldly hound that is known to be a harbinger of death, or psycho pomp, though depicted as green.
There are several names for this entity varying on culture and location. Black Shuck in Norfolk, Barghest in England.
Could all of these entities that are similar, but different be part of or based on one entity? Feel free to add your input, other information, etc.