An "Inject" wad is when you take a Virtual Console wad and replace the ROM inside it with another ROM, such as taking the normal VC OoT WAD and replacing the OoT 1.2 with OoT 1.0. Or you can replace it with a different N64 game altogether. Basically VC channels contain an emulator and a rom, and you can "inject" a different rom file into it. This is not allowed for speedrunning, since 1.0/1.1 OoT running on VC would be faster for some categories than any officially-released copy of the game.
I'm pretty sure that my JP OoT and MM wads are the same way as yours on the menu, with OoT saying "Zeruda no densetsu: Ocarina no toki" or whatever in English lettering and MM having Japanese text, so you might be fine. Your description of the MM main screen is weird, though; it may be an inject of a different version, causing it to emulate oddly.
I don't know much about MM versioning, but I recently added MM to my Wii Menu myself, and I think I saw 1.0 and 1.1 versions. I would just assume the higher number is the real wad, and the other is an inject. I didn't think there were different version numbers, though; when people talk about MM version differences they just compare "Japanese" and "English"... maybe someone else can elaborate. Not sure why ZSR doesn't seem to have a page for it...
Where is the most reliable place to get the correct WADS for speed running? I might just reinstall them altogether