The System.Web.Security.FormsAuthentication
has absolutely nothing to do with Membership. This is used to emit forms authentication cookies and this was class was present since ASP.NET 1.0 and is not specific to MVC4.
The SimpleMembership Provider is indeed a new custom membership provider that was designed for ASP.NET MVC 4 and it uses SQL Server to query the database.
You could still use your custom membership provider in MVC4 without any problems. The Simple Membership Provider was created in order for users that do not have any existing membership provider code to get started with MVC. Since you already have a working implementation with NHibernate I would recommend you using that. The Simple Membership Provider was not intended to be customized that way.