If a major robotic character looks human (is an "android" in the looser sense of the term), there is a very good chance that they will act robotic, being unemotional and uncreative, and given to Robo Speak. On the other hand, if a major robotic character looks completely mechanical, there is a very good chance that they think and act quite human, exhibiting plenty of emotion and saying quite human things even if they say them in a Robo Speak accent.
Apparently, major robotic characters can look human and act mechanical, or vice versa, but seldom show the same nature both inside and outside. This makes dramatic sense: an android that both looks and acts human is hardly different enough to be any fun; a robot that looks and acts mechanical is really more of a prop than a character, unless you put a lot of effort into inserting some interesting behavior, usually human but less obviously so, into the character.
The Spaceship Girl trope is a counter-trope, since she usually both looks and acts human; the audience is only reminded that she's not human when she refers or reacts to her status as a ship.
Examples of androids that act mechanical
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Anime and Manga
R. Dorothy Wayneright from The Big O. Although she is capable of feeling anger/happiness/longing/etc; she is unable to express these emotions to a great degree. Thus, she comes off as a very mechanical Deadpan Snarker.
It's suggested that this isn't a shortcoming of her programming or construction, but the effect the death of her "Father" had on her, which would be a very human reaction.
Unsurprisingly, this was discussed and analyzed by the Tachikomas in Ghost in the Shell: Stand Alone Complex. The Tachikomas notice that while they (the robotic spider tanks) are given nearly human intelligence, the humanoid robots are given much more primitive AI. They surmise that this is because humans are uncomfortable with the idea of a robot being both human-like in intelligence and form, as that makes it too close to actually being a human being when it is, in fact, not one. As such, the Tachikomas acting human doesn't bother people because of their obviously inhuman appearance, but if they were given human form, people would be scared of them.
Subverted in the short series Time Of Eve: In public, androids have holographic rings over their heads, act quite unemotional, and tend to only follow commands. Thinking of androids as or treating them similar to human beings is considered at least nerdy, or highly taboo. But in the Time of Eve cafe, where the rule is not to distinguish between humans and androids, it is impossible to tell who is which, and their true personalities are let loose.
To be honest he doesn't act that weird for an 8 year old body with only a 2 year old brain.
Daryl, another android boy, from the 1985 movie D.A.R.Y.L.
Averted by Bishop in Aliens, whom neither Ripley nor the audience would've realized was a synthetic (all right, artificial person) if he hadn't cut his finger. Subverted by Ash in the first film, who successfully passed for a human who was as stiff and unemotional as an android.
Chip from Not Quite Human, a robotic teenager. Although he averts the classic behavior to some degree (he has free will, understands emotions and can use subterfuge to trick people), he exhibits many robotic quirks, such as limited facial expressions, twitchy movements, and decorating his dorm room with posters of famous robots. His robotic girlfriend Roberta qualifies even more, since she lacks Chip's experience and free will. For instance, she was not the least surprised that he too was a robot, since a statistical extrapolation of her limited social group back in the lab would suggest that roughly one in five persons was a robot.
In the Robin Williams movie Toys there is an android that, while looking human, doesn't really act like a robot at all. She doesn't really act NORMAL, either. She acts like... well... a crazy person? Crazy in the dumb funny way.
The T-800 (Mark II) in Terminator 2 slides along the scale...when he first shows up looking just like a normal Badass Biker, he is almost as inhuman as his predecessor from the first film. As the film progresses, the more banged-up he gets, with his robotic half showing, the more human he starts to act.
Justified in a deleted scene where John and his mother take out his CPU and reset the switch, allowing him to learn and function as more than just an automaton.
Miss Willow, a "femiquin" (prostitute robot) from Fritz Leiber's novel The Silver Eggheads. Contrast with Zane Gort and Miss Blushes from the same novel, in the next list.
Inverted in Alan Dean Foster's Cachalot, where a stiff-necked, unpersonable government official is rightly judged not to be an android, because any decent android would've been programmed to act more friendly than that. In short, he was "too mechanical to be mechanical."
This trope is presented in the show as the reason for his slightly off appearance, as well as for his unemotionalism and inability to use contractions.
His Evil Twin Lore still has pale skin but has fully emotions and can use contractions. He was considered the flawed prototype, with the deliberately less human Data being the perfected final model. Though the main flaw was being evil, of course.
Vicki, the little android girl (little gynoid?) played by Tiffany Brissette on the TV show Small Wonder.
Rhoda the Robot, played by Julie Newmar on the mid-1960s TV show My Living Doll.
Examples of mechanical-looking robots that act human
Anime and Manga
Again in The Big O, we have the piano-playing robot, who, unlike Dorothy, speaks exactly like a human and shows the full emotional range that a human would have. He was built to play the piano so well that he taught Dorothy how to play with subtle nuances. In the second season, we then come across a mechanical detective; he has built-in equipment for forensics, but aside from that, he approaches cases in the same way a human would. He also takes on this particular episode's case for personal reasons. While there are other androids and gynoids disguised as humans, neither of these two attempt to hide what they are and are treated as professionals in their fields.
The Mons of Digimon are actually computer programs, and are all shapes and sizes, from fluff-balls to Humongous Mecha to Cosmic Horrors, but act very human (or at least, display a human level of mannerisms and emotions.)
The Tachikomas in Ghost in the Shell: Stand Alone Complex are sentient tanks that manage to act cute and human, despite looking like giant blue mechanical crabs on wheels with multiple eyes around their bodies.
In the episode "Machines Désirantes", this trope comes up as a subject of conversation among the Tachikomas themselves. One of them theorizes that, as advances in cybernetics technology blur the lines between humans and machines, humans are becoming nervous about any robots that seem too human. Thus, any robots which require a human-like appearance (in order to interact with human environments) are given less advanced AIs so they're not perceived a threat, while more advanced AIs are confined to obviously non-human bodies. note What originally sparked this philosophizing was the worry that Major Kusanagi was displeased by the Tachikoma's emerging self-awareness. And she was, but not for the reasons they thought: the Major simply thought that it would be a liability having robots on the battlefield navel-gazing.
Star Wars: Played with in C-3PO and R2-D2. Threepio is specifically designed to be an "interface" between humanoids and roboty-robots, and thus is more human-looking and -acting than most droids. Artoo, by contrast, is entirely inhuman and speaks in beeps, but has a much more relatable personality.
Averted by Robbie the Robot, in Forbidden Planet, who is very definitely mechanical, both in form and manner — though his polite, robotic personality is not without its charms.
Zane Gort and Miss Phyllis Blushes, robot lovers from Fritz Leiber's novel The Silver Eggheads. Contrast with Miss Willow from the same novel, in the previous list. The dichotomy is rationalized by Zane, who tells the human hero that, if you tried to cram all the AI circuitry of a real robot like himself into the same chassis with all the human-mimicry devices of a "femiquin," the result would have to be 10 feet high or as fat as a circus fat lady.
Just about all of Isaac Asimov's robots except R. Daneel Olivaw, but especially Robbie, from the short story "Robbie", the first story of the "I, Robot" anthology.
In the Hitchhiker's Guide and Starship Titanic universe, the designers give robots and other mechanical things that speak "Genuine People Personalities" which are copies of people's personalities.
In the futurist book 2081, there are laws that prohibit making androids that can be mistaken for people, mostly for safety reasons (e.g. so rescue workers will know to save the humans first). How much different they need to look varies from country to country.
Keith Laumer's "Bolo" series of stories all revolve around tanks that start about the size of houses and move up from there. Their AIs are modelled to be courteous Warrior Poet types, to offset the fact that a groupone of them could sterilize a planet. You don't WANT strange, alien mindsets running around with your guns, after all.
To the point that they are usually more moral, ethical, and all-round better people than the flesh-and-blood humans who give them orders.
The commentary mentions that she was supposed to look like an inverted The Birth of Venus, which she does for a certain angle. Some fans ignore this, as the commentary mentions this in the past tense.
Bondage is just cooler?
GLaDOS went through many, many designs before the final idea. One looked like little more than a gigantic flying saucer. Even the concept sketches for the 'Birth of Venus' model look robotic enough to satisfy this trope.
While most sentry guns have a limited (still makes you want to spare them) set of responses, the defective ones in Portal 2 just don't get enough time to show their personality.
Defective turret: I'm different.
However, a non-defective turret in the last co-op level yells a unique and coherent statement, and they all can apparent make an opera.
Some of the personality cores have a surprisingly human behavior. If they aren't chanting Madness Mantra, that is.
Wheatley, despite being literally a ball, has a very developed personality.
Robo-Ky from Guilty Gear XX, particularly in Accent Core Plus, besides his ridiculously Robo Speak vocabulary, has a very Jerkass personality, an identity complex involving Ky Kiske (whom he was based on), and quite the libido.
The Chee of Animorphs .They look mechanical without their holograms, but act human. Turn on the hologram, though, and no one can tell the difference, meaning they usually both look and act human.
Tony Stark's robot helpers in the Iron Man movies are plain mechanical arms with no dialogue, a few sound effects, and minimal expressiveness. They get most of their character from how Stark interacts with them.
Al and Sulla from O Human Star both look and act completely human. Brendan's Gimel 75 butler plays it straight though; he looks robotic but acts fairly human.