There's no such formt in the world called DVDR, but it is used widely as a term describing "recordable DVD discs", whichever their format. To be more precise, most of the time the term DVDR refers to DVD-R and DVD+R formats, but quite often also to DVD-RW and DVD+RW discs.
The term is used so vaguely because all of the four main "DVDR formats" (DVD-R, DVD+R, DVD-RW and DVD+RW) have the same storage space and because all the software tools that handle burning to recordable DVD media, support all four formats. Thus, it is safe to use the term in phrases like "Converting DivX to DVDR", meaning that the target format is the same (MPEG-2) and the amount of data that can be burned to disc is the same (same as in regular DVD-5 disc) and "Burn that movie to a DVDR".
Related glossary terms
Related software tools
DVDREasy is a free program that automates the multiple steps to backup DVD9 to DVD±R.
ImgBurn carries on from where DVD Decrypter left off! (Well, for the burning part anyway!)
VSO ConvertXtoDVD (Shareware)
Easy-to-use tool that allows converting any video file format (DivX, AVI, WMV, ..) to a DVD-compliant video.