Why do Windows and Linux see different files on a DVD ROM?

I'm not sure this is the correct answer, but maybe it'll provide you with details that will help you.

It could be because MS-Windows and Unix use different file systems on DVD - even on the same DVD. Files on an optical medium are usually arranged using a file system protocol specified in the ISO 9660 standard (also see notes at the end).

But the standard allows for extensions, and Microsoft has designed their own extension to the standard called "Joliet" that allows Microsoft Windows compatible operating systems to read different file names with more features (longer names and support Unicode) than the standard ISO 9660 file system allows.

For Unix-style operating systems (such as Linux), another extension called "Rock Ridge" was developed, to allow even longer file names, Unix-style permissions, and a few other things.

It is very common to have both Rock Ridge and Joliet extensions on the same optical medium, but it could be that the creator of that DVD used these extensions in a clever way to only have the MS-Windows related files show in the Joliet part of the system and only have the Linux specific files show in the Rock Ridge part of the system. The isoinfo program discussed in this stackexchange answer might provide more information.

Notes:

As mentioned in the discussion in the comments, while a lot of media are still authored in ISO 9660 and its extensions where the kinds of tricks discussed in the OP can happen, ISO 9660 is obsolete and modern media should be authored using UDF (ISO 13346) which is a Universal Disk Format and only allows a single view of the entire file system - so such tricks will probably not be possible on a UDF authored disk.