DVD-ROM and DVD+R question

What is the difference between these two formats. I have a new Sony NS325 set top stand-alone player. When reading in the instruction booklet it says that one of the disc that the player will not accept is DVD-ROM. It will accept DVD-Video, DVD-R/RW in video format, and DVD+R/RW. So far, the only media I have ran through it is DVD+R and it has been flawless. I purchased some Maxell DVD-R media that was on sale and plan to burn it using my NEC 3500. I can select to burn it as DVD-Video using Nero, so I not concerned here. Is it that the older DVD players worked off of the DVD-ROM format? Also, if I had an older player that accepted DVD-ROM, what format would I use? Would I chose DVD-ROM(ISO), DVD-ROM(UDF), or DVD-ROM(ISO/UDF)?

Sorry for the noob question and thanks in advance for help.

It’s like how you can’t put a game CD into your home audio CD player and expect any results. The game CD is CD-ROM and the player is wanting CD-Audio. Your DVD player also can not do anything with DVD-ROM since it is designed to play DVD-Video. It doesn’t know what to do with ROM data like computers use.