i don't know a lot about the subject, but the little i know tells me this is not the way to look at this

your password (plain text) is secret because only you are supposed to a have it. in the digital realm, sharing the contents of the password (plain-text) is be akin to making a copy of it — undesirable

now, the algorithm that hashes the plain-text for comparison with the stored hash, that can be know by anyone, and typically is

so password ≠ hashing algorithm

Yes. Password and hashing algorithm are distinct things. I fully agree with you.