Would it be illegal for a company to tell some employees that the company is not giving out ANY promotions (promotions come with a salary increase), or annual merit increases to salary, and then give out promotions and merit increases other employees. The company is saying one thing, and doing another.

What is the difference in the ones they are telling? Like are they all doing the same type of work? Or is it more like a favoritism thing?
What is in any contracts or employee handbooks?

I don't think it is illegal but it may not be ethical.

The employees all work in the same department, and all have the same type of job. Also this is in Arizona so there is no contract, it's a right to work state. Some employees were given raises, and others were told that no one in the entire department is getting a raise or promotion because of budget reasons.

They can really do whatever they want then.
Companies can make any decisions they want as long as it follows federal and state law.
With ''right to work'' states it basically means if you don't like the way things are done you can go find another job.