That's effectively what gets cut, but in terms of physical cutting and reproduction, it's simply 2 coils 90 degrees from each other, each 45 degrees off vertical, one for each channel. They are wired so that an in-phase signal (i.e., same signal in both channels; mono) moves the stylus laterally, while a completely out of phase signal (i.e., mono but with the polarity flipped in one channel) moves the vertically. If there's a signal in one channel but not the other, one groove wall has modulations and the other doesn't, and the effective stylus motion is at a 45 degree angle.
Matrixed formats are just a stereo signal, so nothing changes. CD-4 used an ultrasonic FM modulated signal to encode the rear channel difference information (with both the front and rear channels being cut in stereo normally). In a most basic sense, cutting and playback is no different from the basic stereo cutting described above, except the cutting and playback systems have to be able to handle frequencies up to 45kHz to preserve the FM modulated rear difference signal. Of course, when cutting at half speed, the cutting equipment would only have to be able to handle frequencies up to around 22.5kHz. But as far as the cutting and playback styli are concerned, they are just dealing with stereo signals that happen to have very wide bandwidth. It's the encoder and decoder that combine/split the audible and ultrasonic content.