CD and DVD drives are also called optical drives because unlike other types of computer drives which operate with magnetic bits, CD and DVD drives use optical sensors and lasers to burn and read dips in plastic disks.
A CD ROM or DVD ROM is a type of drive that reads CDs or DVDs.
A CD RW or DVD RW drive can both read or write to those media.
You may often see DVD+/-RW which indicates that the drive can burn both plus (+) and minus (-) DVD disks. There is little difference today between the two types of disks, however if you have a DVD+RW then it will only be able to use DVD plus (+) disks.
On top of plus and minus DVD formats, there are also dual or double layer (DL) DVD's which hold twice as much information as regular disks.
Now, there are also High Definition DVD's which hold even more than double layer disks. Originally there were two types of high definition disks: HD and BlueRay. The current market has eliminated HD from being used on new release DVD's so BlueRay seems to have won the format war much like VHS dominated BetaMax. There are still many HD DVDs around but it may be more beneficial to use BlueRay DVDs in the future.