CD's and DVD's are called optical disks. Writing data onto optical disks is often called "burning".
The only difference between CD's and DVD's is how much data they can hold. CD's can hold up to about 700MB per disk. Normal DVD's can hold up to about 4.2GB per disk. There are also dual layer and double sided DVD's which hold more.
CD-R, DVD-R and DVD+R disks can only be written to once. If the recording goes wrong, that's a wasted disk, often called a "coaster" because jokingly it can only then be used as a drinks mat.
CD-RW, DVD-RW and DVD+RW disks can be written to, and then later erased and written to again. Therefore if you're not used to writing data onto optical disks, buy some CD-RW disks and experiment with them, erasing them when you want to try again. Once you've gained confidence use -R disks for permanent backups.
There are two ways of writing data to optical disks. One writes all the data, using a program such as those published by Nero or Adaptec/Roxio. The other way is to write each set of files separately using Windows Explorer. I find the first option much more reliable but if the second works for you it's probably easier.
These days there's effectively no difference between DVD- and DVD+ disks. They were originally two rival systems but all modern equipment can read and write both types.
HTH, John