BDSM: an acronym compiled from bondage and discipline (BD), domination and submission (DS), sadism and masochism (SM). It is a type of consensual sexual play between adults. Wikipedia summarizes the distinction between consensual and nonconsensual play in a clear, concise manner that took me two seconds to look up:
The fundamental principles for the exercise of BDSM require that it should be performed by responsible partners, of their own volition, and in a safe way. Since the 1980s these basic principles have been condensed into the motto "Safe, sane and consensual", abbreviated as SSC, which means that everything is based on safe, sane and consenting behavior of all involved parties. This mutual consent makes a clear legal and ethical distinction between BDSM and crimes such as sexual assault or domestic violence.
Fic example:
Dualism by Isabel3029
slavery: a system under which a person is reduced to property and forced to work against their will. Human trafficking is a form of slavery that was defined by the United Nations in The Trafficking Protocal:
The recruitment, transportation, transfer, harboring or receipt of persons, by means of the threat or use of force or other forms of coercion, of abduction, of fraud, of deception, of the abuse of power or of a position of vulnerability or of the giving or receiving of payments or benefits to achieve the consent of a person having control over another person, for the purpose of exploitation. Exploitation shall include, at a minimum, the exploitation of the prostitution of others or other forms of sexual exploitation, forced labor or services, slavery or practices similar to slavery, servitude or the removal of organs. The consent of a victim of trafficking in persons to the intended exploitation set forth [above] shall be irrelevant where any of the means set forth [above] have been used.
A fic example that understands this:
A Voice in the Darkness by katinki (which I highly recommend you read if the distinction between the two is still unclear to you.)
A fic example that does not: any fic in which Bella is a slave (and is therefore incapable of giving consent) that tries to pass it off as BDSM play.