A natural harmonic is when you mute a harmonic node and pluck the string. They can be performed only on open strings.
An artificial harmonic is the same, except that you artificially shorten the string length by fretting, and move the node up accordingly.
A pinch harmonic refers to "pinching" the string, using the edge of your right (picking-hand) thumb, and your guitar pick. The string is muted (producing the harmonic) with your right thumb, and plucked with the pick, while your left (fretting) hand holds down the fret. A pinch harmonic can be performed on either artificial or natural harmonics. You can also do pinch harmonics using the right (plucking) hand index fingernail, instead of a pick, and still muting with your right thumb.
Here's a lesson from YouTube:
http://www.youtube.com/watch?v=5I5O8P-r5Rk
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