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For reference, I make these damn drives for a living.

From a consumer point of view, there is NO practical difference between DVD+R and DVD-R.  They both run just as fast and store just as much.  They are both SUPPOSED to be compatible with the majority of DVD readers and in practice are, but some systems have problems reading one and some problems reading the other.
And, of course, some drives write plus, some write minus and most new ones write both (at varying speeds - 16x/16x are more expensive)

DVD+R is intended to look identical to a DVD-ROM when closed.  Like a CD, once you close it, you can't write to it any more.  In its technical advantages it uses the same system for writing the technical info at the start of a disk (which says how big the disk is etc.) as it does for writing the main user data.

DVD-R uses a 'wobble' at the beginning of the disk to encode its data.  This makes it harder to lock onto at higher speeds.  (This problem is now solved, though.)

both plus and minus use the same basic laser technologies - the hardware is the same.  However the chip may need to be different (to cope with reading the wobble)

Lastly - a comment on 'book type'.  This is a bit of data that tells a drive what type of disk it has got.  There are special codes for plus and minus.  HOWEVER - most old dvd readers don't understand anything other than plain old 'DVD' in this slot.  So if you've got the option, set it to that.  Most writers understand that you have to lie in this field.  (However some older writers will then refuse to let you write to such a disk, thinking it's a ROM.  Argh!)

+RW (rewritable) technology exists for both plus and minus.  It works about like you'd expect, but is again harder for ROM drives to read (since the disks have to be made of different stuff so that you can erase them)

RAM is different.  DVDRAM is NOT a normal DVD.  If you look at it, you ca see this.  The disk is divided up into lots of concentric rings with blocks of black stuff at varying distances.  It looks a bit like one of those old secret decoder rings.
These black blocks allow the drive to very quickly (in theory) to lock on to the desired bit of data, even if it's not anywhere near where you are currently reading.  Modern drives don't really need this help.
What they DO allow you to do is erase just a single block of the disk, rather than a whole track.  This makes them more easily used in the same manner as a VHS tape (over-recording as you go, rather than wipe clean and start)

RAM is also built to be used more like a hard-drive.  This mainly manifests itself in the terminology used, but also means that it has a VERY robust defect management scheme.  It has both 'when the disk is made' handling for errors, that tell it that specific bits of the disk should ACTUALLY be read/written in a different place. 
This is quite complex, and in many ways unimportant since a DVD disk is much cheaper thn a hard drive, and partially failed ones are just thrown away.  (The lower capacity is a factor here as well)
It also has real-time handling, that says 'this block is bad, skip it and pretend the numbers didn't go up'.  This IS useful, though somewhat painful for us drive manufacturers.

Plus and Minus both have a similar 'defect management' scheme - it is called Mount-Ranier.  (MRW for short)  This works pretty much the same way, a list of bad areas is kept on the disk, as well as where they should be read from.  It is drive specific how you decide a given bit of the disk is going bad (typically due to a scratch) and choose to remap it.  Any MRW reader should be able to cope with any MRW disk, however.  Disadvantage?  Almost NO ROM drive will.  So don't use MRW for movies, only for data.

The 'make your disk look like a floppy' with instant erase and drag-and-drop functionality etc. is called by microsoft Mount-Ranier, but this is actually just done in the operating system and can work on any type of (RW) disk.  It's pretty much the same as DirectCD?.  Only for DVD.  And marginally less likely to crash your system.

Really REALLY technical details (my speciality is ATAPI, not the disk level) provided to non-competitors on request.

Question: is there a particular combination of DVD+R media brand / DVD burner / software / burn speed setting that you would recommend as being most likely to produce DVD+Rs readable in older / less reliable drives? - MoonShadow
In general, a slower write is safer - but many newer burners do NOT like to write slowly.  8x is a good speed.  As for media, you get what you pay for - but ALSO try to get media that existed when the drive firmware first came out.  Drives have to be tuned for specific media and produce lower quality disks if they have to fall back on their 'generic' methods.  Software really REALLY shouldn't matter unless you are getting underruns.  All the software does is throw out a bunch of write commands.  Having said that, nero is superior at letting you get under the hood and tweak options.  All you REALLY want is 'close disk' and 'book type' though.  --Vitenka

Question: those "buffer underrun prevention" tickboxes you get in CD/DVD authoring software - how do they actually work under the hood? What happens when the buffer empties - AIUI writes have to happen as one unbroken lump? - MoonShadow
This is drive dependant - however most new drives can do a true 'seamless link' where the engine stops writing at the end of one block and starts writing at the start of the next one, making it impossible to distinguish from a non-underrun write.  The quality of the write, and of the link, varies of course by drive.  (And by instance of drive.)  Ours are, of course, the best ;)  --Vitenka
Addendum.  Most, if not all, DVD burners ignore the setting of this checkbox and will do seamless linking whether you like it or not.  The theory is that a seamless disk is better than a coaster.  On the one hand, this is a good indication of how stable we believe the technology to be.  On the other, you may want to be sure your software logs underruns whether the burn is aborted or not.  (Nero express does NOT do this, you have to watch the bar.)  --Vitenka

There is another alternative.  Older drives would use variable-packet writing to cope with gaps in the writing, inserting a link sequence of seven blocks which the application (supposedly) knows how to skip over.  This mode very rarely works without a user-layer table of contents specifying where these links are.  (I say rarely because an application can detect a link sequence and skip over it when it encounters it, but it messes up the whole addressing scheme unless you are designed for it)  DVD-ROM drives can't really cope with this well and so drives that do this as underrun protection should be jettisoned.  Luckily, nothing made in the last few years does.  --Vitenka

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