You will lose your save state, yes, but that refers to the "auto-resume" memory dump that the Wii captures when you exit the VC.
Your game save [as created through normal game operations, like saving your city in Sim City, or hitting "Save and Quit" in Mario 64] are written to physical files that can only be deleted in the memory management utility.
Think of "state" as "what the software was doing at the second I left the program" and your save game as "the last time I hit "save" in the actual game." I alternate between using one or the other myself. ["State" is a lifesaver in Sim City, because you skip the whole "year of power outages / no police protection" bug that you would normally encounter from resuming a save.]