There are two main formats: “dash” (DVD-R/RW) and “plus” (DVD+R/RW). There’s not much difference between them. They both record data and video, and they both read back data and play back video. Both formats are available as recordable drives for computers and as home video recorders. In spite of claims that one format is more compatible with players and drives, both formats are similarly compatible. There are speed differences, but it’s a game of leapfrog. One format will come out with faster write speeds, then the other one will match it or surpass it. 16x is the theoretical maximum speed, so the latest drives from both formats are close to the limit.
Modern “combo” drives can write to almost all disc formats (DVD-R, DVD-RW, DVD+R, DVD+RW, CD-R, CD-RW). Older drives write only their DVD format, so you may have to get DVD+R/RW discs for a DVD+RW drive and DVD-R/RW discs for a DVD-RW drive.
The DVD+RW format has a few advantages when used in a computer, but if data backup or access speed is important, also consider the DVD-RAM format. DVD-RAM is fast and reliable, and the discs have an optional cartridge to help protect data. Most DVD-RAM drives also write DVD-R/RW discs, and some “super combo” drives write all three formats.