Q: if "My Computer" says I have a DVD/CD-RW Drive, does that mean I have a DVD Burner/Writer? Or just a CD Burner?
A: you have a CD burner, not a DVD burner. If anyone says otherwise I would ask them to do their research.
CD-RW is a cd burner
DVD-RW is a dvd burner
In your case, a DVD/CD-RW means it can do the following:
-Read DVD's
-Read CD's
-Write CD's
If this is for a laptop, and you want a DVD burner, you might consider buying an external on www.newegg.com or if you have a desktop, then you can swap it out with a DVD burner, which now are pretty cheap.
There are two interfaces for desktop DVD burners, the IDE (wide ribbon) and SATA (narrow ribbon). If you have a desktop that is only a few years old, it may have SATA capability, thus you would want to buy a SATA drive. The narrow wire helps with the case airflow and isn't as cluttered as the IDE versions, unless you get special cables.
Yes, complicated, but if you have a laptop, your going to buy an external that connects to your laptop via USB port.
Hope that helps!
edit:
I am getting kinda annoyed that there are people here who have no clue what they are talking about. They honestly need to hit the books before they start giving misleading responses.
Burner and writer are the same things. It means you stick in CD+RW, CD-R and it will burn onto them.
If you tried to put in DVD-R, DVD+R, DVD-RW, DVD+RW, then you will find they can't be burnt.
You can stick in a DVD movie and play it, but you can't burn it.
The difference between +R and -R is confusing, and all you need to do is know to buy the minus version because its the m