SNM:
Spanking isn't always BDSM play, but neither are bondage (cops do this to criminals), whipping (many slaver societies have historically used this to keep the slaves in line), or stockades (this was an accepted punishment for many petty crimes in medieval Europe).
I agree with you mostly, the whipping you mention would be similar to the parental discipline I mentioned, punishment rather than BDSM, although I think that kind of thing can straddle the line sometimes if one or more of the participants is genuinely sadistic or masochistic (not "play" as such but definitely an aspect of BDSM - I don't classify punishment as "play" in any event). If by stockades you mean stocks, pillories and the like then yeah its obvious that modern versions are taken from the original punishment versions (not a particular favourite of mine, they are uncomfortable if one is a little on the short side like me), the same would apply to many of the implements we use in modern BDSM.
I personally have never heard any BDSM enthusiast calling spanking "vanilla", however it does tend to be one of the examples we use when trying to get across to vanilla friends some idea about how WIIWD, trying to provide examples of very mild aspects of BDSM that the majority of couples have tried at some time to give them something they can relate to
