A SQL Server database instance is simply a named installation of SQL Server. The first that you install on any given machine is usually the default instance, which does not have a specific name - you simply connect to it using the name (local) or the name of the server machine.
SQL Server Express is usually installed as an SQLExpress instance, so the instance is called SQLExpress, and you connect to it using (local)\SQLExpress or .\SQLExpress or MyServerMachine\SQLExpress .
SQL Server instances are completely independent of each other, and you can basically install as many as you want - you just need to use unique instance names for each. But when you start the SQL Server installation again, it will show you which instances are already installed and offer you a new instance name for the new installation. There was no harm.
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