Broadwell-S definitely existed, but was cancelled and replaced with Haswell Refresh. Broadwell-C was a preminum model that was also meant to be available. So in 2015 they originally intended to only release Broadwell-C that year for desktop but the yields weren't good enough for a chip that big... so they ended up pulling in Skylake-S since it was ready. Even then, the 6700K was unavailable for months.