• Actually, There's no difference between fragment and fragmentActivity in terms of their objective. Both are doing same but in different ways.
• If your app targeting a platform version before honeycomb, you need to use fragmentActivity class which holds your fragment because earlier versions of android doesn't support fragment class.
• If your app targeting a higher version of API (higher than honeycomb), you can use fragment class. This fragment is hold by activity.
• If you are using fragmentActivity, you have to import the android.support.v4.app.Fragment package.

          Or

• If you are using fragment, you have to import the android.app.Fragment package.
• Both classes has different methods to get the Fragment Manager.

         For Fragment class the method is,
                 getFragmentManager()

For more information, Click Here