depends on who you talk to.
I always think of natural harmonics as the ones at the 5th, 7th and 12th frets. You touch the string and pick it and get a natural harmonic.

Touch harmonics are bending a note and touching the string an octave higher.

Pinch harmonics are squeezing your pick and finding the sweet spots over the pickups.

Feedback harmonics are sounding a note and then moving your guitar around until the amp starts feeding back.

Tap harmonics are holding a chord and tapping the string an octave higher.