Ask HN: "key derivation function" vs. "password hashing algorithm"

Trying to get my head around the subtle difference between a key derivation function (like PBKDF2) and a password hashing algorithm (like bcrypt or scrypt).

Not really wanting to start a religious war over which is better or worse - I'm just trying to understand what the difference is between the two techniques. I read that PBKDF2 shouldn't be used for storing passwords, then elsewhere I read that all kinds of different people and places do exactly this.

Crypto is not my strong point in my day job, and I promise I'm not implementing a homebrew crappy encryption algorithm on my own, I'm just trying to understand this difference well enough to explain it to someone here who's asking.

If PBKDF2 shouldn't be used for password hashing, if I use PBKDF2 to derive a key from a passphrase, what do I do with this key in order to get a password hash I should be storing? Passing it to a hashing function seems kind of counterintuitive to me.

If I pass that passphrase to bcrypt, I get a password hash that I can store. I got that far. There's just some intermediary step between of "derived key in, password hash out" that I seem to be not understanding.