Differences between Classic Mode and Claims based Authentication

            Classic Mode Authentication: It refers to the integrated windows authentication. You cannot configure the Forms based authentication if your web application is using Classic Mode Authentication. You can convert a web application from Classic Mode Authentication to Claims Based Authentication. However, that can only be done using PowerShell commands and its an irreversible process.

            Claims Based Authentication: SharePoint 2010 is built on Windows Identity Foundation. It enables authentication from windows as well as non-windows based systems. This also provides the capability to have multiple authentication in a single URL.