In ArcCatalog, "Database Servers" refer to workgroup installations of ArcSDE using SQL Server Express.
You can do all of those things you listed using a workgroup installation of ArcSDE - managing it all from ArcCatalog.
In ArcCatalog, "Database Connections" refer to enterprise installations of ArcSDE.
As of 10.0, you can only connect to an enterprise ArcSDE database and assign permissions to existing users. Creating additional databases in an enterprise ArcSDE environment is currently done at the Database Server level via ArcSDE post install, or if you wanted to use sde command line.