sqlsever2008 and above description of each installation package

LocalDB (SQLLOCALDB)
LocalDB is a lightweight version of Express, which has all the programmability features, but runs in user mode and features a fast 0 configuration installation and fewer prerequisites required. You can use this version if you need to create and use a database from code in a simple way. This version can be bundled with application and database development tools such as Visual Studio or embedded with applications that require a local database.
Express (sqlexpr)
The Express version contains only the SQL Server database engine. It is best suited to situations where you need to accept remote connections or manage remotely.
Express with Tools (SQLEXPRWT)
This package contains everything you need to install and configure SQL Server as a database server, including the full version of SQL Server Management Studio SP1. Choose LocalDB or Express according to your needs.
SQL Server Management Studio Express (Sqlmanagementstudio)
This version does not contain a database and contains only tools for managing instances of SQL Server (including LocalDB, SQL Express, SQL Azure, full version of SQL Server Management Studio SP1, and so on). You can use this version if you have a database and only need administrative tools.
Express with Advanced Services (SQLEXPRADV)
This package contains all the components of SQL Server Express, including the full version of SQL Server Management Studio SP1. The download size of this package is larger than the "with tools" version because it also contains both full-text search and Reporting Services.

sqlsever2008 and above description of each installation package