What is the difference????
 

I have seen PS2 backups advertised as DVD-R and CDR, amongst others.

What is the difference in the formats?

The PS2 games come in two different formats:
DVD-Rom
Compact Disc

The backups you are talking about cover those two formats.
DVD-R for the DVD-rom games
CD-R for the compact disc games.

A DVD-R hold roughly 4.7 gb of data.
A CD-R holds roughly 700 mb of data.

So basically you could put 6 cd-r's on 1 DVD-R....

Thats the main difference, the amount of storage on the discs.
(They are 2 completely different formats)

this means
if u buy a game on cdr and the origanal was on dvdr it has been ripped
most music will b removed
all fmv will b removed plus other stuff to make it small enough to fit on a cdr

Stick with direct backups, You will have less problems.