I can’t tell you the specifics, but most drives (the majority) write info to the DVD-R formats, useful enough for identification (though it might only give you an internal name that doesn’t match up with the model used to market the drive).
Comparatively, very few drives can or do write the same information on DVD+R formats, and if they do, it’s often less useful for ID.
There are a number of apps that will show you this basic info if available. Nero CD-DVD Speed can get it, ImgBurn can get it, and I think DVDInfoPro can do it. OptiDriveControl might be able to show the info, but I can’t fully remember. So the command exists to retrieve the info.