Actually the four letters of BDSM stand for six words.
Bondage/Domination
Domination/Submission
Sadism/Masochism
It's up to each person to decide what emphasis they put on the various aspects. For some it can be almost exclusively about the giving and/or receiving of pain (S/M). For others it may be the the clearly defined roles of D/S without any bonding or beating coming into it.
As long as everyone is a safe consenting adult there is no right or wrong.
That there are those who feel a “real” dom is… is more comparable to those who Adera talks about as seeing her more like a cock to fuck them rather then a woman who happens to have a penis.
People are all too often idiots.