DVD-R and DVD+R are totally
different format closer to the difference between VHS and Betamax though it looks physically the same from the bare eye.!
DVD-R format (pronounce DVD R or DVD dash R but NOT DVD minus R) is supported by "DVD Forum" and, I believe, came to the market first so likely the most compatible with most DVD players. Major member of "DVD Forum" includes Toshiba and Pioneer. DVD+R format is supported by "DVD+RW (Read DVD plus RW alliance) and major members are Philips and Sony.
For DVD-R format, you use DVD-R for write once only (

CD-R) and DVD-RW for rewritable (

CD-RW) ie, recording more than one time

a cassette tape in the old day.
For DVD+R format, you use DVD+R for write once only and DVD+RW for rewritable.
In the old days, the DVD recorder only supported one format. However, I believe the line became blur and some may now be called universal 'recorder' for DVD-R and DVD+R format.
There are another lesser known "format" for DVD recordable called DVD-RAM which is mostly used in computer but also supported by Matsushita (Panasonic and JVC). DVD-RAM is more

a hard disc and floppy as you don't need special software to burn it. However, the disc is in a special catridge

some CD player in the car in the old day so you need special reader to read it and a regular DVD player will not support this one.
You can see more info here
http://en.wikipedia.org/wiki/DVD#DVD_types