Both Twitter handles and .sol domain names are a part of SNS, yet are slightly different. A Twitter handle can only be claimed by the owner of the Twitter account. In order to guarantee this, the user needs to tweet the wallet address they want to associate with the account and then sign a transaction using the same wallet address. An oracle then verifies that the public key contained in the tweet matches with the signer. In practice, this means that Twitter names are already reserved. Twitter users just need to claim their public key by tweeting it.