When it comes to simple CD ISO images it is possible to burn them to a DVD+/-R, but what about the more general case? Is it possible to copy a CD with audio tracks to DVD+/-R? What about mixed mode CDs that contain a data track? What about those old hybrid CD that contain also a Mac filesystem?

Using the DVD in a CD-only drive will of course not work, but would it be possible to make it work in a PC that contains a DVD drive? How compatible are CD-R and DVD-R in general? What things does one support that the other doesn't (aside from one having 700MB and the other 4.7GB)? Basically what are the use cases for which one would still need a CD-R in these days and couldn't use a DVD-R as replacement?

Edit: And an additional question: Who decides if a CD is an audio-CD or data-CD, is it the OS that interprets the data one way or another or does that difference already happen in the drives firmware?