The answer is yes.
In your Sony desktop CD-R drive you can use only CD-R or CD-RW discs. No DVD
disc.
In your laptop, you have a DVD+RW drive. It is probably not only a DVD+RW.
It is probably a dual drive (CD and DVD) and so you can use a CD-R disc to
copy to a CD-R disc, or a DVD+R disc to copy to a DVD disc.
The procedures are different.
To copy to a CD-R disc, you can use XP. No problem.
You cannot use XP to copy to a DVD+R disc.
In order to copy to a DVD+R disc you need specific software capable of doing
this. Since your laptop came with a DVD drive, you should have the software
to do this already installed on your laptop. If not, the most popular
software to copy to DVD discs are Roxio and Nero but many other available
and they can be used to copy to both CD and DVD.