You sure know a lot about socialism and words, for someone that doesn't know that these social democrats are called so because it's literally the name of their parties.
But the whole point, on my side, is to emphasize that in some cases "socialist" means "authoritarian communist" (that's been only when the word is used by some Americans) and in some cases (the most of the time e.g. if you are dialoguing with somebody from Europe) it means something else. See my other comments for more.