Biography
A sadist is someone who enjoys the suffering of others. While a sadist who has a good sense of morality and empathy will stick to playing a Cruel Player-Character God or doing some Casual Kink in a Safe, Sane, and Consensual way, sadism becomes outright Nightmare Fuel when combined with sociopathy. This is the kind of character that takes pleasure in inflicting Cold-Blooded Torture and psychological abuse. Whether it's physical or psychological, a sadist will take pleasure in making or seeing others suffer. Sometimes, a sadist has a Lack of Empathy that stops them from feeling any guilt from the suffering they cause. However, that is not a prerequisite: Some of these characters do indeed feel bad about their actions; they just enjoy it too much to stop.
Note that while real-life sadists are usually of the decent kind and psychiatry stopped perceiving sadism and masochism as mental disorders long ago, fictional sadists are usually of the truly despicable kind. After all, a sociopathic sadist is much easier to use for drama or for eroticized daydreaming. When the non-sociopathic kind of sadism is included in fiction, it tends to be either for a plot twist, some lighthearted fun, or maybe even tragedy.
The original Trope Namer is the author Marquis de Sade, who in his books used sexual sadism both for fetish fuel and for satirical ways of describing the hypocrisy and injustice rampant in pre-revolution France. Back when psychiatry viewed all sexual minorities (including homosexuality) as "mental disorders", regular BDSM was considered pathological under the diagnoses "Sexual Sadism" and "Sexual Masochism". For a little while long ago (in an appendix to DSM III, but not included in the later versions DSM IV or DSM V), psychiatry also had a concept of non-sexual sadism as a mental disorder of its own. Sadist characters may or may not fit any diagnosis, or in the case of sympathetic characters, be unfairly labeled with such a diagnosis.
Many sadist characters are not physically violent, and the ones who are usually come from a violent culture or background. Psychological and emotional sadism is much more common and, in some cases, much more sophisticated and harmful, being easier to disguise from either the victim or their loved ones. It's also, often, very mundane — the Mean Boss, The Bully, and the Domestic Abuser are all common types of sadists. Many target family members in particular, as they are "safe" targets they can control easily, or otherwise go after someone who is in their power (e.g., a Mean Boss with their employees, or a Sadist Teacher with their students) so that it becomes harder for them to resist. Others, including the nastier types of internet Troll, prefer to target strangers and may hide their behavior from those closest to them (at least, if they feel they will be judged for it), essentially leading a double life.
The difference between The Sociopath and the sadist is that the latter wants to hurt others; the former is defined by their utter indifference and lack of remorse, and typically cause harm only as a means to an end. A sadist is not necessarily devoid of guilt; rather, like the Narcissist, they just ignore or find excuses for it, frequently blaming their victim ("You're stupid"; "you're weak"; "Why Did You Make Me Hit You?", etc). That being said, the two disorders are highly co-morbid, meaning that there are plenty of sadistic sociopaths and sociopathic sadists both in fiction and in Real Life. When sadism meets narcissism, the results are equally ugly. Serial Killers and, indeed, many violent criminals and personalities, often have shades of all of the above. Many sadists won't see or even consider the idea that there is a problem with their behavior. However, sadism just gives you unusual appetites rather than removing your sense of morality — there are heroic sadists out there who either suppress their desires or find socially acceptable outlets for them.
The difference between this trope and a Blood Knight is that a sadist may not even enjoy fighting. They simply love the misfortune of others. Whereas a Blood Knight will enjoy fighting his opponent (and are likely to lose interest if their target is unable or unwilling to fight back), most sadists will be perfectly fine with torturing a helpless victim. Expect them to take extreme actions to make their victim suffer as much as possible. That said, there are plenty of characters who fit both bills. The Heroic Comedic Sociopath is usually this trope Played for Laughs. See also It Amused Me (which may or may not include torture), Soft-Spoken Sadist, and Unsexy Sadist. An easy, psychologically realistic option to explain a villain who does things For the Evulz — in fact, most characters who don't have some more abstract or alien reason for adhering to that trope will be sadists who let their appetites rule them. Frequently overlaps with Ax-Crazy, The Sociopath, Mad Doctor, Sadist Teacher, Depraved Dentist, Blood Knight, and Loves the Sound of Screaming. Compare and contrast with Combat Sadomasochist, who's just as happy with receiving pain as dishing it out. Dystopia Justifies the Means and To Create a Playground for Evil often involve sadistic delight in the misery of a whole setting.
A sadist is quite capable of delving into Stupid Evil if they take their joy for harming others over actually choosing the more intelligent decision. In fact, many villains have sadism as a Fatal Flaw, choosing to make their enemies suffer and drive them to despair instead of just shooting them and getting it over with.