Sign in with Twitter is the pattern of authentication that allows users to connect their Twitter account with third-party services in as little is one click. It utilizes OAuth and although the flow is very similar, the authorization URL and workflow differs slightly.
What is OAuth?
OAuth is an authentication protocol that allows users to approve application to act on their behalf without sharing their password. More information can be found at oauth.net or in the excellent Beginner’s Guide to OAuth from Hueniverse.