A COMMAND-SPONSORED Dependent is a Dependent residing with a member at an OCONUS location at which an accompanied-by-dependents tour is authorized, the member is authorized to serve that tour, and who is authorized by the appropriate authority to be at the member's Permanent Duty Station. If you are stationed in the CONUS with your sponsor then you are NOT a command sponsored dependent. If your sponsor gets "deployed" OCONUS then that does NOT make you a command sponsored dependent. Here is a sample Command Sponsor Letter. A Non-COMMAND-SPONSORED Dependent is a dependent prohibited from traveling to overseas commands at Government expense. In other words, you are not on your sponsor's PCS orders to an OCONUS location (e.g. Korea). Here is a sample Non-Command Sponsor Letter.
What is a "command-sponsored and non-command sponsored dependent?"