In most states in the U.S. all employees can be terminated at will. It is generally called "right to work" (yes... it is a questionable name). So essentially that first category does not exist in the U.S. (outside of a union where it gets tricky). So the Labor Secretary's decision amounts to the same decision.

And self-employed here generally are not taxed less, rather about the same (details vary), but have to do the taxation themselves.

I should note that you still can be fired illegally, for example surrounding harassment or protected status (gender, race, etc...).