SQL Server is a service so it requires the SQL service which runs as SQL Server *
where the asterisk is the instance name. That is the database and is the minimum you need to connect using SSMS. If you are using SSIS then that is a separate service. Same thing for SSRS. If you have enabled full text searching in SQL and need that then there is yet another service for that.
In general you should have the SQL service running as Automatic so it always runs. The remaining services can be set to Manual so they start on demand. The SQL Server VSS Writer
needs to be running as well for backup and recovery.
Note that you cannot create a shortcut to the SQL Service because it is a service. It is run from the Services
MMC snapin and requires admin privileges to manage. You should leave it running all the time unless you only rarely need to use it in which case you can start it (from an elevated command prompt or MMC) when you need it. You don't need anything else running.