"1) The DVD-R (pronounced "DVD dash R") and -RW media formats are officially approved by the standards group DVD Forum. The DVD Forum was founded by Mitsubishi, Sony, Hitachi, and Time Warner, so it has tremendous industry support for its technical standards.
2) DVD+R ("DVD plus” R) and +RW formats are not approved by the DVD Forum standards group, but are instead supported by the DVD+RW Alliance. The DVD+RW Alliance is supported by Sony, Yamaha, Philips, Dell, and JP, so it also has tremendous industry support for its technical standards. Note that Sony supports both organizations."
DVD+R is a newer standard for how data on a disc is burned/read. It has better error prevention, both in writing to the disc and reading the disc. Most DVD players can read either just fine as a practical matter.