Most 3D discs will be Blu-Ray, not DVD. Yes, the file format is different for 3D than for 2D. If you download Stereoscopic Player (free trial version) for your PC and run your disc through your PC with your 3D display hooked up to it, you might be able to see what kind of 3D your DVD has on it.
Some of the 3D file formats look the same as 2D formats when you look at their file names in a directory. Examples of those would be side-by-side, top-bottom, and interleaved. Those would also be the most likely ones to be on a DVD, so viewing it through Stereoscopic Player would probably be the easiest way to find and use the particular 3D format used.
Or, maybe your DVD has an anaglyph 3D format which uses the colored glasses. That would not utilize the 3D display for 3D - it would work as well as it can work on any kind of color display.
The 3D on Blu-Ray disks has a different format from 2D, and you can identify that by looking at the files in the directory, if you know what to look for. Almost surely, a DVD would not have that frame packed file format, though, as there would not be enough room on a DVD for very many minutes of 3D video in that format.