Cat and dog fleas are different species of fleas. However, cat fleas can live on dogs, and dog fleas can live on cats. It is also near impossible to tell which is which just by looking at them with the human eye. If you have a microscope at home, you can tell the difference, but other than that, you need to know where the fleas have originated to know which species they are.
Cat fleas are the most common species around the world, but more common in North America. However, despite the name, they usually come from other outdoor wild animals such as foxes, skunks, raccoons, etc. The cat flea, or the Ctenocephalides felis, also uses human contact to survive and can live on humans in their hair.
Dog fleas, or Ctenocephalides canis, are less common, but they will affect all sorts of animals, including cats, dogs and humans. Mostly found in Europe, they are still found on wild animals like foxes and raccoons.
No matter which flea we are talking about, the Ctenocephalides canis or the Ctenocephalides felis species, they both carry parasites such as tapeworm, which will infect dogs and cats alike.