I grew up in Utah, hunting fishing, and camping, basically anything in the outdoors was my life. They went to the draw system there in the late 90's because of the amount of non-resident hunters coming there. All the hurds there from Deer to Moose etc... were dwindling fast.
However what the draw system did (at least back then) was limit there area where you could hunt. Basically you put in a draw for multiple areas for specific game. Then you would normally draw a tag from one area; which in turn took you out of the draw for the rest of the state for that animal. I am not sure if it's the same way anymore, they may have tightened down on it even more.
The only thing I remember for sure is that the Moose hunts were once in a lifetime. Meaning if you got a Moose tag then you had that one chance to get a moose. If you didn't use that tag that was it no more putting even putting in for it. I heard a while back though that they changed that from you can continually put in for a tag but once you get a moose you can't ever get a tag for it again.
The current residents of that state may be able to help you out more but I am hoping that this sheds some light on what you have read. Deciphering Utah's laws and regs can be a big pain in the

I guess that is why I quit being a cop there and moved clear across the country.
Anyway my rant aside I hope I have helped you out