In more modern terms we like to speak about erotic power exchange (EPE) or BDSM (bondage, domination, sadism and masochism), rather than use terms like sadomasochism. This distinction is used in order to try and distinguish forms of eroticized power play from other, unwanted, behavior.
Erotic power exchange is social role play, revolving around the power element that forms a part of every relationship between human beings. Hence it is not - although often depicted as such - a purely sexual game. In fact many people will identify it as a lifestyle and, sociologically speaking, one might even identify it as a separate culture or at least subculture. Erotic power exchange identifies the power element, magnifies it and uses the power dynamics between partners as one of the instruments to build and shape a relationship. It is usually - but not always - connected but not restricted to the sexual activities between partners in a relationship.
What identifies erotic power exchange from sadomasochism (as widely acknowledged by the psychiatric community, probably most prominently in the Diagnostic and Statistical Manual of Mental Disorders IV - the latest diagnostic manual published by the American Psychiatric Association in 1992) is the freedom of choice for both partners to enter into forms of erotic power exchange. The choice to engage in erotic power exchange as well as the choice of role are non-compulsive are both voluntary. It is usually driven by very deep personal emotions and it should be safe, sane and informed consensual, based on mutual respect and trust and (not always!) love. Next, the partners within erotic power exchange should adhere to certain basic rules known as the concepts of erotic power exchange, such as discussing and negotiating each other's wants, needs, emotions as well as negotiating and acknowledging emotional and physical boundaries. In other words, erotic power exchange is role play by free and voluntary choice of the participants, as opposed to any situation where either of the partners has no choice or is forced or manipulated into a role.
Unfortunately, erotic power exchange is often judged or described based on outdated definitions, as formulated by Krafft-Ebing, Freud, Schrenk-Notzing, Lacassagne, Thoinet and Eulenburg, some of which date back to the previous century. As a result of this, dominance and submission within an erotic power exchange context are often described as "sadism" and "masochism"; terms (and clinical definitions) which have been formulated to describe mental distortions, not sexual behavior. Sadly, for several decades everybody either involved in or trying to describe erotic power exchange activity has - and many still do - used these terms as well, thus only contributing to the unfortunate confusion of tongues which forms the basis for stereotyping and social stigmatizing.
Next to this - given its individual character and determination - erotic power exchange is very hard to describe in a few words. Hardly two erotic power exchange couples or situations are alike, which makes it impossible to try and describe the activity in a few simple terms. Every simplification will almost automatically lead to oversimplifying and thus stereotyping. For example, erotic power exchange is often mistaken for algolagnia ("pain lust"). Pain can be, but does not have to be an erotic component. Using pain in an erotic setting is only one of the very many rituals or conventions power exchange can have.
Contributing to the confusion even more - especially to the outsider - is the effect know as the "safe haven syndrome". The erotic power exchange community in general is very tolerant and as a result will often be a (temporary) safe haven for others who may be attracted to some of the aspects of erotic power exchange but not all of them and who are mainly attracted by the tolerance within the group. As a result of this the community is rather overcrowded with people that are into pain kicks (algolagnia), transvestites and fetishists, but also with people from entirely different fields, such as parts of the science fiction culture.
Since erotic power exchange - the main instrument of which is symbolism in almost all forms and shapes as long as it is in some way connected to power - can have all sorts of elements, "borrowed" from other kinks so to speak, these connections are not entirely illogical. In a commendable effort to be non-discriminatory but sometimes overly politically correct (a type of social behavior quite natural to any group who is itself the victim of discrimination and stigmatizing) the erotic power exchange community has failed to identify itself from others and only recently subgroups within the community - such as the homosexual and Maledom/femsub groups - are identifying and carefully exploring their own identity and mutual differences in culture, although this is far from widespread yet.