Difference between SQL Server Express versions?

There is a info page .

SQL Server Express with Tools

It is the database plus some tools to help with maintenance in SQL Server Express, LocalDB, and SQL Azure.

SQL Server Management Studio

Only the SQL Server administration tools but not the database.

SQL Server Express LocalDB

This is a different version that is not installable. It is called directly by the application without having to install (it does not run as a service). It is lighter and a bit more limited (it does not have filestream , replication and does not allow remote connection). It does not include administration tools.

SQL Server Express with Advanced Services

The most comprehensive, Reporting Services, Full Text Search and other components.