The fact that it's been "written" on the back doesn't mean it's a RW - but let's say for sake of argument that the disc really is a DVD-RW.
If you've erased it, and re-burned it with blank data, then it's gone. Physically, I mean. DVD's are not magnetic, so if the data has been overwritten it's really gone, unlike a magnetic medium like a hard disk or thumb drive.
It doesn't matter. Whether you have DVD-RW or DVD+RW, the basic operation is the same. Neither are DVD RAM. DVD RAM allows you to edit data on DVD much like you edit data on a hard drive. DVD±RW does not. With DVD±RW, old data must be erased if you write new data to the disc.