DVD-R Authoring vs General Discs
This only applies to DVD-R !! The DVD Forum devised the two disc formats called "General" and "Authoring". Pioneer was the forerunner and have sold more DVD-R drives than any other company - by far.
History
The original DVD-R disc was developed in the late 90's. It was expensive, and was used by corporations to create just a few discs for kiosks, seminar presentations, etc. It used a 635 nm laser beam and the capacity was 3.95 GB.
Later it was decided that a new format was needed for the public, using a 650 nm laser with 4.7 GB capacity. They kept both formats - renaming the original to "DVD-R Authoring" and the new format was called "DVD-R General". In addition, the Authoring format capacity was increased to match that of the General format, at 4.7 GB. They each had certain advantages:
Authoring vs General
DVD-R Authoring 4.7 GB discs - these are capable of storing CMF (Cutting Master Format), which allows the disc to replace DLT master tapes, saving a lot of time and insuring that the original DLT tapes can be stored in a safe place. The disc's lead-in area is used to store the DDP (Disc Description Protocol) - required by DLT master tapes. DVD-R General discs cannot do this.
DVD-R General 4.7 GB discs - contains CSS encryption, making it impossible to burn bit-for-bit copies. Of course, CSS was hacked almost immediately by a 16-year-old.
DVD burners may be specific to one format or the other, as shown below (this table is a bit old - replace DVR-A03 with DVR-A05):

NOTE: you don't really see the 3.95 authoring DVD's around anymore !!
Which format to Buy
For PC users who burn our own DVD-R's - always purchase "General" DVD's". If the DVD-R does not indicate what version it is - then it will be a "General DVD-R". Authoring DVD-R's are a very small, niche market.
Compatibility
Playback compatibility for both formats is universal. Recording compatibility is not. The rule of thumb:
all DVD players can playback both Authoring and General DVD-R discs
Authoring DVD-R burners cannot burn General DVD-R discs
General DVD-R burners cannot burn Authoring DVD-R discs