Unfortunately I have been unable to locate a downloadable manual for a any Daewoo DVD recorder, so can't see how this DVD recorder acts with DVD+RW and DVD-RW.
My assumption would be that the DVD recorder writes using DVD-VR format by default to DVD-RW discs and using a DVD-Video complaint format to DVD+RW discs. While the VR format offers more features than a DVD-video compliant format, unfortunately DVD-VR cannot playback on some DVD recorders. Also on some DVD recorders (such as Lite-On models), it is necessary to enable 'Overwrite' for deleted titles on rewritable media in order to overwrite these.
Just out of curiosity, which model of DVD recorder do you have and also do any options appear when you insert a new blank DVD+RW or DVD-RW (such as menu asking to select the type of DVD to create, initialisation method, etc.)?
So far, the only straight forward way to completely clear a DVD+RW is to erase the disc itself (using the DVD Recorder's Erase tool) or by erasing it in a PC DVD-writer.