Since you seem unwilling to own up to what you said, I will help you out.
Does "...but don't tell me homosexuality is "normal" or that D/S isn't Sado-Madochism" look familiar?
It is sadomasochistic. It's part of the BDSM "lifestyle". You just admitted part of it with your belief that Lady isn't a "bottom", meaning submissive. Tell me the "lifestyle" doesn't include dominance, submissiveness, punishment and/or discipline.
You keep using BDSM as proof that D/s is part of S&M. Both are subsets of BDSM.
The term "bottom" is used to denote a submissive. That is not necessarily S&M.
Dominance & submission is a subset of BDSM. And yes, there can be punishment. Whether pain is involved is negotiated between the Dom and the sub. Personally, I prefer other methods of punishing a dub if she needs it. My play rarely involves pain.
S&M pretty much always involves pain.
Let me see if I can put it in terms you might grasp.
Both oral sex and anal sex come under sodomy. But they are obviously not the same thing. While oral sex may include rimming, it is not anal sex.