This is about ConnectionStrings / ASP.NET MVC with Visual Studio 2012 ultimate & SQL Server Express 2012.
Following up with this tutorial here: http://www.asp.ne
after research/tests it turned out to be as follows:
VS will look at the class name of the DataContext and will look to see if you have provided a connection string with the same name as the class name; for example:
public class MovieDataContext : DbContext
and
if it manages to find a matching connection string it will create the DB based on the criteria you specified in the respective data string (to add the DB to the App_Data set the path of the DB to |DataDirectory| as shown in both connection strings mentioned in the question); if the name doesn't match or you didn't provide any connection string, VS will fall back to the default settings and will create the DB in the default location/settings (usually C:\Program Files\Microsoft SQL Server\MSSQL11.SQLEXPRESS\MSSQL\DATA).
note neither the "Integrated Security" settings nor the "Initial Catalog" play any role with this (I was able to create the DB in the App_Data with both Integrated Security = True & Integrated Security = SSPI and with/without Initial Catalog).
Hope this helps. Thanks for everyone that participated.