Nintendo's title (Wiiware and VC) are compatible with both Wii and vWii.
Homebrew title use a specific NAND loader for Wii, and another one for vWii. The .wad can be installed, but the channel will not work if you try to launch it. (it will not brick your console because of the wrong NAND loader)
If you have a homebrew made channel for Wii and you want to use it on vWii, you need to convert it.
There are already a LOT of converted channels you can use.
See here for existing converted channels to install on vWii, and also learn how to convert to vWii yourself :
https://gbatemp.net/threads/forwarders-are-back.340226/