Microsoft SQL Server LocalDB
Usually you can install the Microsoft SQL Server LocalDB as a feature within SQL Server Express.
The Visual Studio Installer will also install the LocalDB as part of the Data Storage and Processing workload.
LocalDB installation copies a minimal set of files necessary to start the SQL Server Database Engine. Once LocalDB is installed, you can initiate a connection using a special connection string. When connecting, the necessary SQL Server infrastructure is automatically created and started, enabling the application to use the database without complex configuration tasks. Developer Tools can provide developers with a SQL Server Database Engine that lets them write and test Transact-SQL code without having to manage a full server instance of SQL Server.
The LocalDB is great for developing purpose so you do not have to deploy a full SQL Server. The LocalDB will also be used in my following post to test WS-Federation authentication for an ASP.NET Core Web Application (MVC).
Connect with SQL Management Studio to your LocalDB
You can connect with SQL Management Studio to your LocalDB as follows.
Server name: (LocalDb)\MSSQLLocalDB
Connect with Visual Studio to your LocalDB
You can also connect to your LocalDB directly from Visual Studio and the SQL Server Object Explorer.
SQL Server Express LocalDB
SQL Server Express LocalDB Reference
Create a database and add tables in Visual Studio