black-tie, white-hat or smoking

I got (and hopefully gave too) quite a brilliant stash of fancy and unique gifts this year and one of the many creative ones I got was this vest from my parents. It's tailored like a formal garment but has the addition of a hoodie to make it truly functional. Though leagues better, it reminds me of those tee-shirts from an earlier age printed like a neck-tie and a dress shirt, and would indeed make a waist-coat to complete a tuxedo ensemble. It German, such a specific suit and dress-code is referred to as a Smoking, rather than a tux (named after the exclusive Hudson, New York neighbourhood Tuxedo Park) after the English-term smoking-jacket—which is a bit misleading since I think of a smoking-jacket as lounge-wear, a bathrobe or something that Hugh Hefner has made his signature outfit.
 Just before the holidays, H and I went to party that was headlined with a local cover-band who called themselves No Smoking—not Rauchen verboten! but rather we realised later that [wir tragen] kein Smokings, which was a little confused in itself as the band was dressed with mismatched black jackets and white shirts, and I think even one member wore one of those tee-shirts with a bow-tie and vest.