In the comics:
The Earth-616 (comics) version of Thanos has been described as a "mutant" Eternal within the Official Handbook of the Marvel Universe.
Source of superhuman powers: Thanos is a mutant member of the race of superhumans known as Eternals, who has augmented his innate abilities through bionic and mystical techniques
Official Handbook of the Marvel Universe Master Edition #10
More precisely, he was born with a genetic disposition known as "Deviant Syndrome", giving him an abnormal appearance and skin tone compared to other Eternals, including his own family, whose physical appearance closely resembles that of humans.
THANOS: Alars, the Mentor, and his wife, Sui-san, were wise and just rulers. They had high hopes for their two sons. My younger brother, Eros, never let them down. But I was an outcast from the start. Born with the genetic disposition known as Deviant Syndrome, I would never be accepted among the Titans as normal, let alone one day replace my father as their leading citizen.
Thanos Vol. 1 #1
To avoid any confusion, despite Thanos having Deviant Syndrome, the text in the Official Handbook of the Marvel Universe (quoted above) still classifies him as an Eternal (homo immortalis) -- albeit a mutant one -- rather than a Deviant (homo descendus).
In the comics, Eternals, Deviants, and humans (homo sapiens) are sister races to one another, all three having been created by the Celestials, via the genetic manipulation of early hominids.
IKARIS: It began with the coming of the gods to Earth when it was populated only by the beasts of the field! Still, it was the presence of life which drew these cosmic beings to this planet. Their huge space-vessel surveyed the land -- and descended... it was then that the gods proceeded with their mission... they chose to change the destiny of a life-form new to the evolutionary chain -- the ape! A specimen was trapped and taken alive. Only the instruments of the gods could do what was done in that momentous time! To the ape was given the cosmic chemistry that would father races to come! In this manner, the dawn ape became the common ancestor of three powerful new species... the Deviant! An ever-changing and destructive failure. Structurally unstable, each new generation of Deviant appeared in new and monstrous ways. His lot was constant war. The human! This species bred with true balance of structure and disposition. Although he was a destroyer, the human was capable of building for peace. His kind was destined to inherit the Earth. He belonged to it. The Eternal! He was more a child of the gods than of the Earth... for he reached for the universe! The Eternals bred few in number and were immune to time and death! They lived apart from all other living beings.
Eternals Vol. 1 #1
Also, as a mutant Eternal rather than a mutant human, Thanos definitely isn't the X-Men variety of mutant (homo sapiens superior).
In the MCU:
In The Art of Avengers: Endgame, Ryan Meinerding says there was a point during the development of the "script" -- likely meaning the script for Avengers: Infinity War -- where they were planning to show more of Thanos' backstory, including him as a baby, and his looking "malformed compared to the rest of his family".
"There was a period of time when they were writing the script where you were going to see Thanos' backstory," Meinerding says. "You were going to see him as a baby, you were going to see him born to a family where he looked malformed compared to the rest of his family, and then you were going to see him on a planet that's crazy overpopulated. And he's walking through, and he's having an actual teen moment of being that seven-foot-tall awkward teenager and everyone's looking at him like, 'Who is this? Who is this awkward kid?' We were also going to see him make an appeal to the government of his world and say, 'We are overpopulated. We're going to end up destroying ourselves. We have to kill half the population, or do something else with them.' And of course, they tell him he's crazy and send him to a prison on a nearby moon. And then he was going to see his whole planet go up in flames because it destroyed itself, and he had seen it happen. So that was the journey, and we were trying to reverse engineer Thanos' design to younger and younger."
The Art of Avengers: Endgame
Another page from that book features concept art of Thanos standing next to what is presumably his immediate family, similar to the page I posted showing the comics version of Thanos standing next to his parents and younger brother. While the other people in this image all look similar to one another, Thanos has a very different skin tone, somewhat different facial features (particularly around the chin area), and is larger in height and build than the others.
In an interview with Entertainment Weekly, Josh Brolin stated that Thanos' "apparent insanity" stemmed in part from the fact that other Titans, including his own family, all looked similar, while he was born "deformed"; a "freak".
ENTERTAINMENT WEEKLY: What is it that damaged Thanos? Where does this pain and anger come from?
JOSH BROLIN: He’s different from his family. They’re all Titans and they all look similar, but he was born deformed. You see how he grew up, you see he was like the Quasimodo of this time, or if you’ve ever read Perfume [Patrick Süskind ‘s 1985 novel about a serial killer who craves beautiful scenes but is disgusted by the smell of humanity], it’s a great parallel to Thanos. He stuck out. He was an anomaly. He was a freak. And that lent to this apparent insanity.
Josh Brolin says there is heart within the murderous Thanos of Avengers: Infinity War
Spoilers below for Eternals (2021):
During a mid-credits scene in Eternals (2021), Eros/Starfox shows up, and is introduced by Pip the Troll as "the royal prince of Titan" and "brother of Thanos". Eros also addresses Thena, Makkari, and Druig as "my fellow Eternals", and is shown to be in possession of a Celestial Communication Sphere, like the one by possessed by Ajak and Sersi.
All of which seems to confirm that the MCU version of Thanos was both an Eternal and a former prince of Titan, as he is in the comics. The fact that every other Eternal in the film, including his brother, is depicted with a human-like appearance also reaffirms the notion that Thanos' physical characteristics were malformed by the standards of his race.