SQL Server Express (aka. Personal or Workgroup ArcSDE geodatabases, also collectively referred to as "Database Servers")
Based on what you've described, it sounds like you're working with an Enterprise ArcSDE geodatabase implemented on SQL Server 2005. In which case, some administration is performed within ArcCatalog (e.g., the Analyze option for feature datasets, stand-alone feature classes, and tables), and some is performed within the DBMS management tools. Connections in ArcCatalog to enterprise ArcSDE geodatabases do not have an "Administration" submenu option - so what you are seeing is expected.
Hope this helps,
... I understand that terminology is sometimes established for historical reasons that are no longer applicable ...
... I'm not trying to shoot the messenger... you are probably not the one who decided on this terminology. But maybe if I express my frustration to enough messengers, ESRI will realize how confusing the usage is, and clarify documentation by making references to Personal and Workgroup database servers more explicit...
... I found the PDF I referred to above as a result of searching for ESRI documentation on how to perform administration on ArcSDE geodatabases on SQL Server 2005. Can you point me to more detailed information that pertains to enterprise gdb's? ...