wp_hash_password unexpected behaviour

When I run wp_hash_password("password") twice the outputs are different. I was under the impression that this is not how hashes are supposed to work. So how should I use wp_hash_password to compare two hashes?

That’s just not the way it works. wp_hash_password() will always return a different value for the same password due to SALTing.

You are searching for the wp_check_password() function.