I haven't been to Tuva or Mongolia - the places where these styles of singing are traditional - so don't take me as any kind of authority (I don't know how to pronounce any of the terms, for a start).
(Recorded by me - click on each style's name to download an MP3 sound sample)
"Khoomei" is the tuvan word for throat-singing in general, but khoomei is also one specific style. Sing a constant note and try and bring it as far back down your throat as you can - by moving your tongue up to almost the roof of your mouth and then backwards. Then by varying the position of your tongue so that the space just above it resonates differently, you can get different pitches of overtone.
Look at the graph for this sample. You can hopefully see that there are two different dark bands running throughout the whole thing - right at the bottom of the picture is the low, long note I'm singing, and above it is the band indicating the overtones. Notice how it's moving around as I (try to) get different notes with the overtones.
In most tuvan/mongolian throat-singing, you achieve the overtones by changing the resonance of the space between the tongue and the roof of your mouth. In kargyraa you don't do this, but simply open and close your mouth to different degrees if you want to modulate the sound.
You'll notice lots of on-and-off dark bands all over the graph for kargyraa. The reason for this is that the sound is so "rough" and growly. Since it's a lot further from a pure sine wave than ordinary singing is, all these harmonics show up on the graph.
Gentle-sygyt is what I'm calling this one. As far as I know it isn't a specific tuvan/mongolian style - it's quite like szygyt because I'm using my tongue to create the overtones, and the ventricular vocal chords are resonating (VVM), but the ventricular folds aren't completely open and free to resonate. They still seem to sound a note one octave below the ordinary vocal folds, but gentler - they don't dominate the ordinary vocal sound.
The graph for this sample proves that it ain't the same as sygyt: it looks a lot like the one for khoomei, and a lot less rough than the sygyt graph. You can see some "roughnesses" at around 10kHz because of the VVM.