From the Valles Caldera National Preserve Website:
Q:May I enter both the state drawing and the Preserve lottery?
A: Yes. You may enter both. The drawing for the Valles Caldera hunts will be conducted first and if you win access to hunt on the Valles Caldera, you will not be eligible for the public state draw. However, if you don’t win access to hunt the Valles Caldera, your application for other units will continue to be part of the state drawing process.
Q:Is hunting on the Preserve a once-in-a-lifetime hunt?
A: No. You may hunt this unit more than once.
From the New Mexico Department of Game and Fish Website:
Valle Vidal
Limited elk and turkey licenses for the Valle Vidal area of the Carson National Forest and the Greenwood Area of the Vermejo Park Ranch Inc. in Unit 55A are issued by draw only.
Valles Caldera National Preserve
All of Unit 6B is closed to hunting and trapping, except elk and turkey. Limited elk licenses are offered only through a special draw. See page 30.
Basically you can apply for the tag through the state draw with straight up odds of drawing it or you can do the lottery and buy up to 20 chances at $30 each or you can do both.
The Valle Vidal is a separate area and you can only draw that tag applying for unit 55A through the state.
That's my understanding anyway.
I guess I need to start applying for some of these choice New Mexico drawing areas.