It depends on state to state. In California, you can get non-REAL ID if you have at least one form of ID (i.e. passport from another country). Doesn't matter whether you're documented or not.

REAL ID looks different and essentially proves that you are not undocumented.

Visually, there used to be no difference between ID for undocumented and documented, so you can travel freely. My immigration lawyer recommended against traveling to AZ with that ID.

Not sure what it changes in terms of hiring. Even with REAL ID after background check, I had to submit proof that I'm allowed to work in this country.