For example I had about 60mb remaining on internal storage and downloaded a game that is 40mb, then moved the game to sd but I only have 15mb remaining as if it hasn't been moved.
Welcome to Android Central! If you're able to move an app to SD, it's never the entire app--only a portion of it, since key parts need to remain in the Internal Storage to function properly. Also, the download filesize noted in Google Play is usually not the full storage requirement that is necessary once you install it, much like in Windows.