The standard photos which you normally see are taken in boot camp in an assembly line fashion. In the Marine Corps, the Dress Blues you see us wearing are not even real. They are a short version (only the part that shows in the camera exists) and they open from the back. This is so you don't have to take any time to button them up. The whole process takes about 30 seconds.
The ones you see of people in other uniforms are probably higher ranking people in command positions who have command photos taken to be displayed in their command units. They get to choose what they wear for those photographs.
All offical Department of Defense pictures are taken using the top half of a dress uniform. Other pictures you may have seen are not offical DD214 "jacket" material unless they're directly related to a specific job- such as a sniper will wear a ghillie suit.
No, they do not give you a choice- such pictures are distributed to Interpol and other government organizations
