In the US right now one of the most popular ways of identification is the driver's license. That is mostly accepted. . Another ID acceptable at the airport is your passport, military ID or whatever Id issued by the goverment with your picture.The EAd even is issued by the goverment many people are not familiar with that document.
Yes, so far. You can use your driver's license within USA continental. I was advice by USCIS that the person who wants to travel to Puerto Rico or Hawaii even are US territories should carry a travel document (Advance Parole).
Good luck,