§ 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.
§ Classic authentication supports authentication types like Kerberos, NTLM, anonymous.
§ Classic is more commonly seen in 2007 environments.
§ 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.
§ Claims based authentication uses claims identities against a against a trusted identity provider.
§ Claims are the recommended path for new deployments in SharePoint 2010.
§ Forms-based authentication is used when we use Claim based authentication. Forms-based authentication is used to implement customized logic for authenticating users without having to worry about session management using cookie.
§ It gives developer more access to specify which files on the site can be accessed and by whom, and allows identification of a login page.