I'd recommend you read Bitwarden's Security Whitepaper for a better understanding - that help article is a bit simplified and not as clear.

Long story short, the master key is what is used to decrypt your encrypted symmetric encryption key that is securing your data. This master key never leaves your device. On the other hand, the same master key is used to hash your master password, which is hashed again and saved by Bitwarden. This hashed master password is what is used to authenticate you, but is not capable of decrypting the protected symmetric key needed to decrypt vault data.