When I stick an audio CD into my Mac/PC and it mounts on my desktop, and then I double click to open it to see its contents, there is no "ripping" involved. The contents of the audio CD are aiffs. I'm not sure what you are saying that "an audio CD does not contain AIFF files or any kind of file."
An audio CD (ie 'Redbook'), whether it is a commercially pressed disc you bought at a music store or one you burn yourself onto a CD-R, contains 16 bit PCM samples. There is no table of contents and no files of any kind.
A
data CD has files. A disc that contains audio
files is not an audio CD - it is a data CD that contains audio files. If it's an audio CD, you have to use Digital Audio Extraction (aka 'rip') to get them from the CD. Files on a data CD can be copied the same as any other file on a hard disk, floppy disc, USB key, etc.
On Windows, if you view the contents of an audio CD you see 'Track01.cda, Track02'.cda, etc (.cda == cd audio) but they do not contain any audio data at all - it's just a pointer to the actual data on the real CD so that when you double click it, Windows can launch the CD player and begin playing that track as long as the CD is in the player. I suspect that the Mac shows the same thing but names its pointer with a '.aiff' extension.
Here's an easy test: copy that .aiff to the hard disk, remove the CD from the CD drive, and then try to play that .aiff. If it is an audio CD, it will either do nothing or pop up an error dialog.