Ive heard people call gacha plus a mod for gacha club so it will modify the game, but others say it is an independent app with gacha club as the base game. Is gacha plus an actual mod, or is it an app?

Well it's a mod but it installs as a separate app ! Though if you're looking forward to an actual independent app but still inspired by gacha club and having the same concept, I recommend following the news for Chibimation ! :)