Previous terminology
Sexual sadism is the term previously employed by the DSM-III-R, DSM-IV, and DSM-IV-TR, where it was classified as a paraphilia. In these versions of the DSM, sexual sadism pertained only to the infliction of real (not simulated) suffering (p. 530). The condition was renamed sexual sadism disorder in DSM-5. Sexual sadism was the term employed in the DSM-III, classifying the condition as a paraphilia. The DSM-III noted that "the imagery in a Paraphilia, such as simulated bondage, may be playful and harmless and acted out with a mutually consenting partner….In more extreme form, paraphilic imagery is acted out with a nonconsenting partner, and is noxious and injurious to the partner" (p. 267). In DSM-III, sexual sadism could be diagnosed if:

the person repeatedly and intentionally inflicted suffering on a nonconsenting person, to experience sexual excitement
repeatedly or exclusively preferred simulated or mild suffering with a consenting sexual partner
employs extensive, permanent, or potentially fatal suffering to achieve sexual excitement, regardless of the consent of the other person.Sadism was the term employed by the DSM-II. In that manual, the condition was classified as a sexual deviation, which was used to describe "individuals whose sexual interests are directed primarily toward…coitus performed under bizarre circumstances" (p. 44). The term "paraphilia" did not exist in the DSM-II, and diagnoses did not have specific criteria until DSM-III. Sexual sadism was the phrase mentioned in DSM-I as one of the sexual deviations (p. 39), but neither it (nor any of the other sexual deviations) received a specific label or diagnostic criteria.
Sexual sadism disorder is the condition of experiencing sexual arousal in response to the extreme pain, suffering or humiliation of others. Several other terms have been used to describe the condition, and the condition may overlap with other conditions that involve inflicting pain. It is distinct from situations in which consenting individuals use mild or simulated pain or humiliation for sexual excitement. The words sadism and sadist are derived from the French writer and libertine Marquis de Sade, who wrote several novels depicting sexualized torture and violence. Related terms and conditions
Current terminology
Sexual sadism disorder is the term employed by the current version of the Diagnostic and Statistical Manual (DSM-5) of the American Psychiatric Association. It refers to the "recurrent and intense sexual arousal from the physical or psychological suffering of another person, as manifested by fantasies, urges, or behaviors" (p. 696). It is classified as one of the paraphilias, called an "algolagnic disorder" (p. 685), which is one of the "anomalous activity preferences" (p. 685). The formal diagnosis of Sexual Sadism Disorder would apply if the individual has acted on these urges with a non-consenting person or if the urges cause significant distress to the individual. Sadomasochism appears in the current version of the International Classification of Diseases (ICD-10) of the World Health Organization. It refers to the "preference for sexual activity that involves bondage or the infliction of pain or humiliation" (p. 172), and divides sadomasochism into sadism and masochism according to whether the individual prefers to be the provider or recipient of it.