DVD-RW and DVD+RW are competing rewritables supported respectively by the DVD Forum and DVD+RW Alliance. Hybrid DVD drives that can handle both are labeled DVD±RW. They are very popular since there isn't an agreed standard for recordable DVDs. Most modern DVD burners are hybrid drives.
The + and - of DVDR media are racing to find new innovations to out pace each other. While new upgrades and advancements will ultimately benefit the consumer, you should be careful in your purchases if your equipment cannot handle both versions. If you are not sure which one to buy,
DVD-RW or DVD+RW, check your DVD drive specifications.