It should be the same between the two consoles for the most part, other than it being extra important to make sure that the connected controllers are the same when recording as when playing back, and being aware that Wii savestates do not include Wii save files. I'm not sure why you would be getting the result of nothing happening when playing back a recording...
If the game you're trying to TAS supports GameCube controllers, then using a GameCube controller and turning off all Wii Remotes usually results in less trouble. But it is very much possible to TAS games using Wii Remotes. The vast majority of games should work.
If the game you're trying to TAS supports GameCube controllers, then using a GameCube controller and turning off all Wii Remotes usually results in less trouble. But it is very much possible to TAS games using Wii Remotes. The vast majority of games should work.