And there are distinctions between the two: identifying yourself, and presenting identification.
There are also distinctions between walking around and being asked, and driving around and being asked.
Yeah, driving is a separate case entirely. But if you’re walking around on the street and a cop asks you to identify yourself (without arresting you), you legally do not have to respond to him. (Again, whether this is a good idea or not is a separate discussion entirely.) You’re not allowed to lie to the officer, but you don’t have to identify yourself. I am not a lawyer, but this is what I have been told by lawyers.
Also, passengers in a vehicle do not have to present identification if they are not thought to have been driving, IIRC.