In the Disney Mickey Mouse world, Goofy and Pluto are both dogs. However, Goofy is anthropomorphic and verbal, whereas Pluto is not and is Mickey's pet.
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Neither Goofy nor Pluto are real-life dogs - members of the species named either Canis familiaris or Canis lupus familiaris, depending on whether dogs are considered to be a separate species from wolves.
Instead, they are cartoon and comic book characters.
Goofy is a comic book and cartoon character belonging to an imaginary species of humanoid intelligent beings who look like dogs in many respects. Such comic book and cartoon dog-like characters are called anthropomorphic dogs.
Pluto is a comic book and cartoon character belonging to a fictional species of quadruped animals that resemble dogs and don't talk but can behave a lot more or less like a human when the plot of a story or a joke requires it. Pluto is a lot more like a real-life dog than Goofy is, but it would be an error to confuse Pluto with a dog.
The fact that Mickey Mouse sometimes says Pluto is a dog merely means that in the fictional universe of Mickey Mouse stories (see Mickey Mouse Universe and Donald Duck Universe), the word used for Pluto's species is the same word we used for dogs in the real world - or maybe it is a different word in a different language translated into English as "dog".
So Goofy and Pluto are not members of the same species, and neither of them is a member of the real-life species known as either Canis familiaris or Canis lupus familiaris.
Goofy, it seems, was always created to be a human type character, albeit as an anthropomorphic dog. Pluto, meanwhile, is meant to actually be a dog. According to the Disney Archives character description of Goofy (available in archive form here: http://archive.is/ELkav ):
Goofy was created as a human character, as opposed to Pluto, who was a pet, so he walked upright and had a speaking voice (first supplied by Colvig, and later by George Johnson, Bob Jackman, and Bill Farmer).
Rather than thinking of him as a dog, then, it might be more correct to think of him as a human who looks like a dog. This is borne out by Art Babbitt's 1934 character analysis of Goofy (available in full here: http://www.michaelspornanimation.com/splog/?p=2418 ):
It is true that there is a vague similarity in the construction of the Goof’s head and Pluto’s. The use of the eyes, mouth and ears are entirely different. One is dog, the other human. The Goof’s head can be thought of in terms of a caricature of a person with a pointed dome—large, dreamy eyes, buck teeth and weak chin, a large mouth, a thick lower lip, a fat tongue and a bulbous nose that grows larger on its way out and turns up. His eyes should remain partly closed to help give him a stupid, sloppy appearance, as though he were constantly straining to remain awake, but of course they can open wide for expressions or accents. He blinks quite a bit. His ears for the most part are just trailing appendages and are not used in the same way as Pluto’s ears except for rare expressions. His brow is heavy and breaks the circle that outlines his skull.
So, Goofy is a "dog" mostly in name only - his species of anthropomorphic animals (like Mickey and Donald) are actually more like humans who resemble their animal counterparts. Pluto, meanwhile, is meant to be an actual dog.