The key derivation is defined here: https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki#user-content-Public_parent_key_rarr_public_child_key

BIP44 is about how many times that derivation is applied. So, BIP32 can stand on its own, but BIP44 can not. It requires the KDF from BIP32.

Also, you never deviate back to the master key, you can only go forward. It's an important detail, because if that ever were to change, all these privacy improvements would be lost, and also coins at risk in some very rare circumstamces.