Do I need both a DVD-ROM and a DVD burner, in order to copy DVD movies?

No, you can only use a DVD burner to copy DVD movies. PowerDVD Copy will first process your source DVD movie content and store it on your hard disc. Then PowerDVD Copy will eject the source disc and request you to insert a blank DVD disc for it to write to.

However, if you also have a DVD-ROM, it will make the whole process more convenient.