Yes, I mean different brands (Verbatim, TDK, HP, ...), different types (DVD+R, DVD-R), and different rated speeds (4x, 8x, 16x).
Each media also has a MID (Manufacturer IDentification) that can tell you something about who made the disc. This drive will look at the MID to see how to write that disc, and if the firmware in the drive doesn't know about that MID the drive will either fail to write or it will chose a default way of writing that media, which may not give an acceptable result or fail during burning.
You can see the MID of any media you put into your drive by using the Nero CD-DVD Speed program, which comes with the Nero suite. It can be found under Nero Toolkit.