Is It Possible To Copy A Dvd-R Disc To Dvd+R?

I have 24 discs of home movies that are all burnt on Dvd-R media that my cousin gave me. I'd like to make a copy for my other cousin who asked me for them recently. But all I have is a stack of Dvd+R 8x TDK discs... I think I tried copying one of the discs using Nero a very long time ago, and it ended up being a coaster which didn't play. I don't know why the mediums differ, as they're just blank discs to me. Can anyone give me an explanation as to how I can go about burning copies without having to save an iso, or anything to hard drive? I'd like to do it straight from disc to disc.


P.s.
Are Dvd+R's less readable in standalone dvd players? Someone told me not all standalones play them.

 

You are correct in that DVD+R's are not always playable in some stand-alone players.

I have used the "Clone" feature in DVDFab (paid version) to copy DVD-R's to DVD+R's.

 

Well, I use Power ISO, that detects the kind of media present in the burner and that's it!!!