Well I accidently deleted the moderators group, so I created a new one, but it doesn't act as the official moderators group. For example when you check something that only moderators can do it doesn't register to that group, and under all the topics it says controlled by moderators. How do I get it set as the official group so everything looks cleaner and permissions can be set?

You would follow the same thing => here

Yeah, but how do I get the original group back. This one shows check marks in the forums permissions, and the other one showed up yellow that it was able to moderate it.

You need to give permissions to this group again.