this can be a bit confusing. you might want to try a hardware technical web site for more exact help. something like tom's hardware on the web tends to be pretty good.
but i'll try and give you a basic explanation. cd's and dvd's are not the same animals. they are not interchangable. you say you have a cd-rw disk, but a dvd-rw drive. it used to be that you couldnt write a cd-rw from a dvd r/rw drive. on newer models that may have changed, so it would depend somewhat on what you've got installed. but generally, you cant write a cd-rw from a dvd r/rw.
to further confuse the issue, you also have types of cd's and types of dvd's. there is cd -r, cd +r, and cd-rw. there is dvd -r, dvd +r, and dvd -rw. there is also a cd raw, and a dvd raw (i think). those last two arent used much. also, cd -r is now discontinued....or is it +r? i forget. see, this is confusing

it also used to be that you couldnt write +r on a -r drive, and vice versa. same with just playing on them. you had to have the right type cd and the same type drive.
now, the good news is, most newer dvd drives will handle cd's of all types. they'll also mostly handle all types of dvds. but, that's only after a certain date of model. if yours is earlier, then it might not. you'll have to check your manual or readme or whatever documentation that came with the drive, or, check the manufacturer's web site, technical support.
and, just to confuse things a bit more, there is now dual layer or double layer, or double density type drives for dvd's. these have double the capacity of normal dvd's, but you do need the dual or double layer media to make use of it.
all in all, the whole +r and -r were a huge mistake in the first place. i mean, this is just what the consumer needed, more choices he/she doesnt understand.
basically, it looks like you're trying to put a round peg (the cd-rw) in a square hole (the dvd r/rw drive).
my solution to all this was to go out and buy two new combo cd/dvd dual layer burners. i put one in each of my machines so i'd never have to worry about +r, -r and so on again.
K.