Dvd is different kind of storage disc even though it looks same as CD. Hence cd-rw cannot write dvd,while usually dvd-r or dvd-rw will be having facility to write on a cd.

the dvd you watch to and the cd you listen to.

The drives are normally the same CD and DVD is the same drive, and if not it says it on the front of the drive

CD - or DVD ! If it's CD - then yes, if it's a DVD, then nope - the playback machines are different.

A DVD has a higher capacity than a CD