The subject of writeable optical media is vast, so here it is in a
squirrel's eye view (i.e., in a nutshell.)
The essential difference between a CD and a DVD is that a DVD holds much
more data than a CD. CDs and DVDs are called optical media, because they are
written and read with a laser.
As the name implies, writeable optical media can be written to just once,
whereas rewriteable optical media can be erased and rewritten, much like
that familiar floppy disk.
It's not really that simple because, if you know how to do it, you can add
to a writeable disk that already has data written to it. However, once the
writeable disk has been filled with data, it cannot be erased and rewritten,
as can a rewriteable disk.
So far, so good?
There are two standards for writing to DVDs. There is no practical
difference between the two methods (a technophile would scream "yes, there
is!"); it's really just a marketing war. Like VHS vs. Beta, if you're old
enough to remember that. The two standards are "+" (called 'plus') and "-"
(called 'dash', not 'minus'.)
So, in CDs you can choose between CD-R and CD-RW, which are non-rewritable
and rewriteable, respectively. And in DVDs you can choose between DVD+R or
DVD-R and DVD+RW or DVD-RW, which are non-rewritable and rewriteable,
respectively.
There are other formats too, like DVD-RAM and double layer DVDs. And then
there's the red laser vs. the blue laser...but that's something else
altogether.
Rewriteable media came to be because when the first writeable CDs and DVDs
were introduced, they were expensive. It made sense to have a disc that
could be written to and erased multiple times. Today, writeable CDs and DVDs
are cheap as dirt. Today, the only reason for using a rewriteable disc is
for practice. For instance, if you're trying out different things in a video
or audio recording project, instead of going through CD after CD you can
just erase the disk and start over.
Writeable optical media is more stable than rewriteable optical media, so if
you're storing something for the long haul, you want a writeable media. For
backups it doesn't matter much, but I only use writeable media for my
backups. I'll take that extra little bit of security, thank you.