There could be a few reasons.
The first, and most likely, is that your system isn't set up to auto-play a dvd or cd. You can either set it up to do that, or you can open up "My Computer" and select the disc from there.
On windows, you actually need a program to burn a disc with, such as Nero or Roxio. You can make a cd or dvd through windows explorer, but this creates a data disc that usually has a hard time reading on other computers.
One other thing to look out for is that your DVD burner supports the type of disc you are putting in it. DVDs come in 3 different formats. You've got DVD+R, DVD-R, and DVD RW. Some burners can only burn to one or the other, and usually have a hard time reading the DVD if it is the wrong type. DVD+/- R drives can write to both and should be able to read both. You'll want to check the specs of your drive to see what type of discs it can author to and ensure you're putting the same type of disc into your computer.
It sounds more likely, though, that you probably don't have your drives set to auto play and you don't have software to burn with, seeing as you're having the problem with both platforms. If you make these changes and you still aren't able to burn, then you may have a faulty drive. Hope this helps.