What parts of SHA-256 hashing an ASIC miner really does, and what remains a CPU job?

Question

I know that ASIC does not perform transactions ledgering, it is a CPU job.

I also know that SHA256 consists of two logical parts: a digest function, which reduces any big message, like ~1MB block, to 256-bit chunk, and a cryptographic hash, which takes and returns exactly 256-bit per iteration. Does both of these SHA256 parts are performed on ASIC, or only cryptographic one?