The vWii (virtual Wii) is the part of the Wii U's system for Wii mode. Additionally, BootMii and Priiloader are not supported, although there are tools to recover from a vWii brick that can be used from Wii U Mode. Many different homebrew applications will not work on vWii, or will result in a brick if used.
While homebrew can easily be run in the vWii, there are not many ways to exploit Wii U Mode from the vWii. This is due to the fact that there is a clear-only register that determines whether the vWii sandbox should be enabled. Nintendo solved this in the Wii U Menu channel by making it simply restart the console. However, there are a couple of bugs, such as dumping the Wii U's boot0 and the HRESET hack, but none are very reliable for gaining code execution in Wii U Mode.
The vWii has 3 different System Menu versions per region, namely 1.0.0, 4.0.0, and 5.2.0. These differ from System Menu 4.3 in the fact that they are ancast images, they fixed Letterbomb, and access to Wii Settings was removed (Wii Options now goes directly to Data Management).
Wii Settings can still be accessed by installing Forecast Channel dummy or News Channel dummy and clicking the "Update" button on the channel launching screen. This leads to the screen to confirm performing an update, where the update can be declined, returning to Wii Settings. This menu reports version 4.3 for all 3 versions of the vWii System Menu.
With an updated System Menu, LetterBomb does not work on the vWii. Additionally, str2hax does not work, because of the removal of the system settings menu. The same savegame exploits that worked on System Menu 4.3 also work here, although this is not necessary, as a vWii-only exploit known as Wuphax exists. Alternatively, Compat Installer can be used.