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Can you explain the difference between available DVD recordable discs?

Can you explain the difference between available DVD recordable discs?

There is DVD-R, DVD+R, DVD-RW, DVD+RW and to add to my confusion, DVD-ROM!!!

DVD-R is a write-once recordable format which allows excellent compatibility with both standalone DVD players and DVD-ROM drives. There are two main types of DVD-R discs: DVD-R for General Use and DVD-R for Authoring.
DVD-RW media uses rewriteable discs which are rated for more than 1000 rewrites in ideal situations.
+RW, like DVD-RW, is a rewriteable 4.7 GB format, and overall it has similar functionality to DVD-RW. One potential future advantage of the +RW format is the optional Mount Rainier drag-and-drop file access support (also known as +MRW) planned for future versions of Windows. However, current drives do not support Mount Rainier on +RW. The level of compatibility of +RW discs in standalone DVD players is similar to that of DVD-RW. The rewritability of +RW is also said to be similar to that of DVD-RW.
DVD-RAM is a format originally aimed primarily as a data solution, but it is now becoming popular as a video format used by some brands of standalone (non-PC) DVD recorders. Early PC-based DVD-RAM recorders used 2.6 GB discs (or double-sided 5.2 GB discs), but current drives also use 4.7 GB discs (or double-sided 9.4 GB discs). DVD-RAM discs are traditionally housed within cartridges which cannot be opened, so that the media is well-protected. Newer Type II and Type IV cartridges can be opened however, an important feature for those who wish to read these discs in DVD-RAM compatible DVD-ROM drives or standalone DVD players. In addition, some DVD-RAM discs are now sold without cartridges.