What you can't do is use SHA2 with a random salt and call it a day.
I believe the actual implementation gives two output fields as a single value, with that value containing the salt and the hash.
This might be why we appear to be talking past each other - I consider bcrypt to be a salted hash because it takes a salt in the inputs and produces a hash in the output.
The fact that the output also contains the salt is, in my mind, an implementation detail.
You'll avoid this confusion in the future if you don't refer to bcrypt as a "salted hash". Salted hashes are the technology bcrypt was invented to replace.