Mining hardware manufacturers use "Hash rate" to define how fast the mining is with their ASICs, but do they mean 1 sha256 cycle speed or Bitcoin hash speed sha256(sha256(header)); ?
The usual interpretation of "hash rate" is the number of distinct block headers that can be tried per second. So this should include the time needed to:
increment nonce value
increment extraNonce or other coinbase parameters and recalculate Merkle root, when needed (once in every 2^32 attempts)
compute two rounds of sha256
compare the resulting hash value to the target.
Of course the two rounds of sha256 are the slowest part of this process, by far.
As Raghav Sood says, there's no way to know if any particular vendor is actually following this interpretation, but it's so widely used that I'd regard anything significantly different as fraudulent.
As per the Bitcoin wiki, Hash rate or hash per second is taken to mean
SHA256D(data), which is the double round.
It's unclear if all miners follow the same convention.