The default Project template of ASP.NET MVC comes with a class named Microst.AspNet.Identity.Owin.SignInManager. This class is used to authenticate users
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MembershipProvider came with FormsAuthentication in ASP.NET 2.
ASP.NET Identity came with SignInManager in ASP.NET 5.
ASP.NET Identity is a new version of MembershipProvider. It offers a lot more features than legacy MembershipProvider.
For example,
If you do not need all those features, you can stick with FormsAuthentication which can be used without MembershipProvider.