I have been asked for two forms of ID when purchasing a certificate of deposit at an institution where I already had a checking account, other cds, and a safe deposit bank, and was visually known to the staff who were merely following whatever mandate came from higher up.
They declined to accept my CHL as a second form of id. Who knows why. After brief protest on my part, they settled for my AAA card as my second form of id.
Some states do in fact issue both a dl and a none dl id. Mine is one of them. I have both, as well as a passport. As much as feasible in our world gone crazy, I try to avoid giving or showing any of these documents to anyone, for any reason, though that is not always something which can be done successfully. There are just too many opportunities for id theft and document fraud that develop from letting others get your dl number, chl number, state id number, passport number, digital signature, and photos.