The term sadomasochism is mainly used by the media and is hardly represented in the BDSM scene. This is partly due to the rather negative connotation of the word, but also because sadism and masochism are only a small variation of BDSM.
I am dominant and like to live that out in sexual games. But I am not a sadist. I do not inflict pain to intoxicate myself with it, but I experience my sexual pleasure through the submission of the sub to my commands.
Whoever takes the dominant part in a BDSM relationship automatically and by definition has more rights, but also more duties. Because it is up to the Dom both to provide for the safety of the sub