PHP's password_hash function is a wrapper for the crypt function?

The password_hash function looks like a wrapper that adds a high-level layer to the crypt function, since it has a default setting that could be done with crypt manually.

The same thing happens with the password_verify function, which seems equivalent to this:

function password_verify($password, $passwordHash)
{
     return (crypt($password, $passwordHash) === $passwordHash);
}

I'm curious as to whether wrappers are added to crypt in the latest version of PHP.

OBS: I know the above code is insecure because it is vulnerable to timming attack, but it is just a way to try to illustrate the idea. The point is whether it's a wrapper or not. Therefore, security is not the focus of this question.

Thanks in advance.