Your state must be different. Most states will issue a Drivers License, or an ID card, but not both. And I THINK there is a provision in a bill before congress that would ban any state from issuing both. That bill's primary focus is to require states to require proof of citizenship before issuing a drivers license. A side effect of 9-11 since apparently all the hijackers used drivers licenses as ID for their flight training, all issued by states that don't require such proof.
California used to require proof, and if you were a Resident Alien, you could get a license, but it was stamped Resident Alien.
We debated after 9-11 getting ID cards for our kids, but our son was 15 at the time, and already had a learnings permit, so couldn't get an ID, and we could have gotten one for our daughter, but have found passports work better.