Hashing and encryption ARE two different things. In fact though, they are both used when you log into your online banking account.
1. Your computer gets the public RSA key of the server and encrypts the AES key with it.
2. Sends the key to the server together with your password, which is encrypted with AES.
3. Server decrypts AES key, using that key decrypts your password, it hashes your password and compares the resulting hash to its stored hash. If two match, you are authenticated.
Server does not actually store your password, just its hash, this way if hacker steals the list of all password hashes, he still cant log in...