I try to understand the difference between SQL Server Management Studio and SQL Server Management Studio Express
The "full" SQL Server Management Studio is the management GUI (graphical user interface) to work with a SQL Server database and is included in all the paid editions of SQL Server.
For the free SQL Server Express edition, SQL Server Management Studio Express can be downloaded for free from the Microsoft web site (or is include, as well, in the "Express with Tools" edition). As far as I know, as of SQL Server 2012, the two versions are essentially the same and don't have any differences in terms of features or capabilities they offer